when you do an nslookup on the vpn client, does the DNS return the correct record for internal and external resources? Its hard to tell if its a DNS or routing issue based on your description.
If nslookup returns the correct records (which it should) but you can only access internal resources, it's a routing issue. I'm guess in this same routing issue, you've probably configured your VPN client so that all network requests must tunnel through your internet connection, and that the VPN segment doesn't have access to internet eaither through an ACL or specific routing issue.
We use a split tunnle, which works well. Internal DNS server still provide name resolution, but traffic bound for the internal network goes over the VPN where as external traffic goes out the clients internet connection.