It still doesn't work.

Remember that 10.70.7.0 is in a VLAN. I have connected it to bgroup1 (set interface "bgroup1" zone "Video (5)").
This is the situation after checking everything again and after apply your suggestions:
===
CONFIG FILE =======================
set clock timezone 0
set vrouter trust-vr sharable
set vrouter "untrust-vr"
exit
set vrouter "trust-vr"
unset auto-route-export
exit
set alg appleichat enable
unset alg appleichat re-assembly enable
set alg sctp enable
set auth-server "Local" id 0
set auth-server "Local" server-name "Local"
set auth default auth server "Local"
set auth radius accounting port 1646
set admin name "admin"
set admin password "xxx"
set admin auth web timeout 10
set admin auth dial-in timeout 3
set admin auth server "Local"
set admin format dos
set zone "Trust" vrouter "trust-vr"
set zone "Untrust" vrouter "trust-vr"
set zone "DMZ" vrouter "trust-vr"
set zone "VLAN" vrouter "trust-vr"
set zone id 100 "Video (5)"
set zone "Untrust-Tun" vrouter "trust-vr"
set zone "Trust" tcp-rst
set zone "Untrust" block
unset zone "Untrust" tcp-rst
set zone "MGT" block
set zone "DMZ" tcp-rst
set zone "VLAN" block
unset zone "VLAN" tcp-rst
unset zone "Video (5)" tcp-rst
set zone "Untrust" screen tear-drop
set zone "Untrust" screen syn-flood
set zone "Untrust" screen ping-death
set zone "Untrust" screen ip-filter-src
set zone "Untrust" screen land
set zone "V1-Untrust" screen tear-drop
set zone "V1-Untrust" screen syn-flood
set zone "V1-Untrust" screen ping-death
set zone "V1-Untrust" screen ip-filter-src
set zone "V1-Untrust" screen land
set interface "ethernet0/0" zone "Untrust"
set interface "ethernet0/1" zone "DMZ"
set interface "bgroup0" zone "Trust"
set interface "bgroup1" zone "Video (5)"
set interface bgroup0 port ethernet0/2
set interface bgroup1 port ethernet0/5
unset interface vlan1 ip
set interface ethernet0/0 ip 83.0.0.180/24
set interface ethernet0/0 route
set interface bgroup0 ip 192.168.10.218/24
set interface bgroup0 nat
set interface bgroup1 ip 10.70.7.218/24
set interface bgroup1 route
set interface ethernet0/0 gateway 83.0.0.177
unset interface vlan1 bypass-others-ipsec
unset interface vlan1 bypass-non-ip
set interface ethernet0/0 ip manageable
set interface bgroup0 ip manageable
set interface bgroup1 ip manageable
set interface ethernet0/0 manage ping
set interface ethernet0/0 manage web
set interface bgroup0 manage mtrace
set interface bgroup1 manage ping
set interface bgroup1 manage web
set interface "serial0/0" modem settings "USR" init "AT&F"
set interface "serial0/0" modem settings "USR" active
set interface "serial0/0" modem speed 115200
set interface "serial0/0" modem retry 3
set interface "serial0/0" modem interval 10
set interface "serial0/0" modem idle-time 10
set flow tcp-mss
unset flow tcp-syn-check
unset flow tcp-syn-bit-check
set flow reverse-route clear-text prefer
set flow reverse-route tunnel always
set pki authority default scep mode "auto"
set pki x509 default cert-path partial
set address "Trust" "10.70.0.0/255.255.0.0" 10.70.0.0 255.255.0.0
set address "Trust" "10.70.7.0/24" 10.70.7.0 255.255.255.0
set address "Trust" "Video rete" 10.70.7.0 255.255.255.0
set address "Trust" "Video server" 10.70.7.150 255.255.255.255
set ippool "vpn_ippool" 10.0.0.1 10.0.0.10
set user "leo" uid 10
set user "leo" type xauth
set user "leo" remote ippool "vpn_ippool"
set user "leo" remote dns1 "10.70.7.150"
set user "leo" password "yyy"
unset user "leo" type auth
set user "leo" "enable"
set user "vpnclient_phase1_id" uid 9
set user "vpnclient_phase1_id" ike-id fqdn "client.gigli" share-limit 1
set user "vpnclient_phase1_id" type ike
set user "vpnclient_phase1_id" "enable"
set user-group "vpnclient_group" id 4
set user-group "vpnclient_group" user "leo"
set user-group "vpnclient_group" user "vpnclient_phase1_id"
set ike gateway "vpnclient_gateway" dialup "vpnclient_group" Aggr local-id "vpngw.gigli" outgoing-interface "ethernet0/0" preshare "zzz" proposal "pre-g2-3des-sha" "pre-g2-3des-md5" "pre-g2-aes128-sha" "pre-g2-aes128-md5"
set ike gateway "vpnclient_gateway" dpd-liveness interval 30
unset ike gateway "vpnclient_gateway" nat-traversal udp-checksum
set ike gateway "vpnclient_gateway" nat-traversal keepalive-frequency 5
set ike gateway "vpnclient_gateway" xauth server "Local"
unset ike gateway "vpnclient_gateway" xauth do-edipi-auth
set ike respond-bad-spi 1
set ike ikev2 ike-sa-soft-lifetime 60
unset ike ikeid-enumeration
unset ike dos-protection
unset ipsec access-session enable
set ipsec access-session maximum 5000
set ipsec access-session upper-threshold 0
set ipsec access-session lower-threshold 0
set ipsec access-session dead-p2-sa-timeout 0
unset ipsec access-session log-error
unset ipsec access-session info-exch-connected
unset ipsec access-session use-error-log
set xauth default ippool "vpn_ippool"
set xauth default dns1 10.70.7.150
set vpn "vpnclient_tunnel" gateway "vpnclient_gateway" replay tunnel idletime 0 proposal "nopfs-esp-3des-sha" "nopfs-esp-3des-md5" "nopfs-esp-aes128-sha" "nopfs-esp-aes128-md5"
set vrouter "untrust-vr"
exit
set vrouter "trust-vr"
exit
set url protocol websense
exit
set policy id 2 from "Untrust" to "Trust" "Dial-Up VPN" "10.70.7.0/24" "ANY" tunnel vpn "vpnclient_tunnel" id 0x2 pair-policy 3 log
set policy id 2
exit
set policy id 1 from "Trust" to "Untrust" "Any" "Any" "ANY" permit log
set policy id 1
exit
set policy id 3 from "Trust" to "Untrust" "10.70.7.0/24" "Dial-Up VPN" "ANY" tunnel vpn "vpnclient_tunnel" id 0x2 pair-policy 2 log
set policy id 3
exit
set nsmgmt bulkcli reboot-timeout 60
set ssh version v2
set config lock timeout 5
unset license-key auto-update
set snmp port listen 161
set snmp port trap 162
set vrouter "untrust-vr"
exit
set vrouter "trust-vr"
unset add-default-route
exit
set vrouter "untrust-vr"
exit
set vrouter "trust-vr"
exit
====================================
===
REPORT EVENT =====================
2010-02-17 10:58:48 info IKE 82.0.0.1 Phase 2 msg ID e8cb6bf9: Completed negotiations with SPI 156309f6, tunnel ID 32770, and lifetime 3600 seconds/0 KB.
2010-02-17 10:58:48 info IKE 82.0.0.1 Phase 2 msg ID e8cb6bf9: Responded to the peer's first message.
2010-02-17 10:58:47 info IKE 82.0.0.1: XAuth login was passed for gateway vpnclient_gateway, username leo, retry: 0, Client IP Addr 10.0.0.1, IPPool name: vpn_ippool, Session-Timeout: 0s, Idle-Timeout: 0s.
2010-02-17 10:58:47 info Rejected an IKE packet on ethernet0/0 from 82.0.0.1:13891 to 83.0.0.180:4500 with cookies 7c7553d43857317e and 63a4e9ec5c9d6520 because A Phase 2 packet arrived while XAuth was still pending.
2010-02-17 10:58:47 info IKE 82.0.0.1 Phase 1: Completed Aggressive mode negotiations with a 28800-second lifetime.
2010-02-17 10:58:47 info IKE 82.0.0.1 Phase 1: Completed for user vpnclient_phase1_id.
2010-02-17 10:58:47 info IKE<82.0.0.1> Phase 1: IKE responder has detected NAT in front of the remote device.
====================================
===
POLICY LOG =======================
Date/Time Source Address/Port Destination Address/Port Translated Source Address/Port Translated Destination Address/Port Service Duration Bytes Sent Bytes Received Close Reason
2010-02-17 11:00:22 10.0.0.1:50650 10.70.7.150:53 0.0.0.0:0 0.0.0.0:0 DNS 0 sec. 0 0 Traffic Denied
2010-02-17 11:00:21 10.0.0.1:50650 10.70.7.150:53 0.0.0.0:0 0.0.0.0:0 DNS 0 sec. 0 0 Traffic Denied
2010-02-17 10:59:59 10.0.0.1:235 10.70.7.150:1 0.0.0.0:0 0.0.0.0:0 ICMP 0 sec. 0 0 Traffic Denied
2010-02-17 10:59:54 10.0.0.1:234 10.70.7.150:1 0.0.0.0:0 0.0.0.0:0 ICMP 0 sec. 0 0 Traffic Denied
2010-02-17 10:59:49 10.0.0.1:233 10.70.7.150:1 0.0.0.0:0 0.0.0.0:0 ICMP 0 sec. 0 0 Traffic Denied
2010-02-17 10:59:44 10.0.0.1:232 10.70.7.150:1 0.0.0.0:0 0.0.0.0:0 ICMP 0 sec. 0 0 Traffic Denied
2010-02-17 10:59:39 10.0.0.1:56492 10.70.7.150:53 0.0.0.0:0 0.0.0.0:0 DNS 0 sec. 0 0 Traffic Denied
====================================
===
SHREW SOFT CLIENT SETTINGS ==========
Auto configuration: ike config push
Address method: Obtain Automatically
MTU: 1380
NAT trasversal: enable (port 4500)
Keep alive: 15 sec
IKE Fragmentation: enable
Name resolution: all settings on Obtain Automatically
Authentication method: Mutual PSK + XAuth
Authentication local identity: FQDN (client.gigli)
Authentication remote identity: FQDN (vpngw.gigli)
Credential PSK: "the key"
Phase1 Exchange type: aggressive
Phase1 DH Exchange: Group 2
Phase1 Cipher Algorithm: auto
Phase1 Hash Algorithm: auto
Phase1 Key Life Time limit: 86400 sec
Phase2 Transofrm Algorithm: auto
Phase2 HMAC Algortihm: auto
Phase2 PFS Exchange: auto
Phase2 Compress Algorithm: disabled
Phase2 Key Life Time limit: 3600 sec
Policy Remote Network Resource: 10.70.7.0 / 255.255.255.0
Maintein Persistent Security Associations: checked
====================================