You do need Audio for VATSIM to talk on the radio.  But first, you’ll need to resolve the disconnection problem.  If I remember correctly, VATSIM does display a message on why it disconnects: e.g. invalid login password, particular server unavailable, unacceptable/duplicate aircraft call sign etc.  Hopefully, you can find a clue.
After you have obtained a stable connection, then…
  1) Install Audio for VATSIM. 
  2) Find a location in the world where there is a current live ATC service available.  You can install VATSpy, for example to see where services are staffed.  Position your aircraft at a gate on one such airport.
  3) Find and tune the COM frequency for that ATC.  VATSpy also has info on that.
  4) Connect with Audio for VATSIM; and ask the ATC for a “radio check”.
Good luck!