Shannon,
SonicWall VPN can be either a group VPN or single VPN connections. Which are you using?
IS your VPN connection to the firewall (and is it doing NAT?), or are you connecting to another system in the LAN?
If your VPN is to the firewall, once the connection is up the NAT should work and you should be able to see the entire network just like being connected locally, as the VPN connection should put you on the LAN side of the firewall, even with NAT. Browsing, however, is another issue!
I would suggest, especially if you do have NAT in place, that you set up a hosts file on the external system with the internal NAT addresses and names for all the internal systems, or at least for the WINS server and the internal DNS servers so name resolution can be accomplished.
Typically, if you can not browse it is because your system can not resolve the names to internal addresses, ie.e, a DNS or WINS issues, as NATTED server addresses can not be resolved from the outside unless you can redirect the request to the internal DNS or WINS server.
HTH,
David