Matt,
Ya Sounds like a fuel delivery problem.
First thing I would ask is how old is the fuel?
Double check all the fuel lines and make sure there arn't any holes or cracks in them. If you have a fuel filter is it cloged or needs replacing since it can restrict fuel. Also check the float height via kerry's method on the homepage of www.gstwin.com..Everything else is going to involve taking the carbs off which I would suggest anyways because the bike is 11 years old and I'll bet 80% the carbs are just gumed up espicaly if the bike has been sitting for any of those 11 years. Clean out the float bowls really well, check the gaskets making sure their still rubber. FYI while you got it apart at this stage replace the pilot jets w/ 40's. BTW to check to see if a previous owner jetted find the adjustment screw location and see if it has been drilled out.
The only other thing I can think of that something might be swimming in your gas tank that blocks the pea chicken momentarly.
Check your airfilter, too.