When I connect at work the net is going to assign me a dns that is working fine.

After that when I connect to VPN I'm going to receive a different dns. With this one I can reach the server of the vpn owner but I'm not able to go to the internet.

BUT if I switch the dns with the old ones I'm able to surf again (still connected to the vpn, but I cannot surf their server).

Recap:

DNS1) MyPC -> CompanyProxy -> Internet

DNS2) MyPc -> CompanyProxy -> VPN -> NoInternet (can Ping vpn servers)

DNS1) MyPC -> CompanyProxy -> VPN -> Internet (cannot ping vpn servers)

Weirdest thing: I'm able to do a nslookup from anywhere, but ping is going to fail.

Is possible to use both DNS? Or setup a dns just on the browser?

I'm quite lost..