Pontiac firebird 2001 v6 won't start and battery I bought 2weeks ago is already dead what should I check first

i'd lean toward a bad alternator.

Yeah I had taken my car to Sears and they had a special machine that was checking the alternator the battery and the regulator and some other things in your vehicle it was like a computer test and it could tell you weather or not you had a bad alternator or not. They diagnosed my Saturn to have a bad alternator this is years ago but I recommend doing that you could have a short somewhere or hopefully your terminal posts are nice and clean the connections that go to the battery that's important too make sure they're nice and tight clean but maybe you could take it to Sears and get a proper diagnostic because they might be able to tell you whether or not it's the alternator or it's a wiring issue so that's about all I got for you.