while you are VPN connected ; can you try to resolve anything using you local DNS ? ; can you even ping your local DNS ?
i have a feeling that your VPN connection should not filter out any communication with local IP network ? if so then test this criteria by trying to do a DNS query while VPN connected
some thing like
#nslookup
then set the server to your local server
>server my.dns.ip.address
then try to resolve any local DNS name

if the request times out this means that your resolver [DNS client] could not communicate with your DNS server ! ; if not then this means that you will need to add the local DNS to the list of valid DNS servers that is used while you are VPN connected [this is related with the configuration acquisition that is made upon VPN connection ]

regards