Scott--
I haven't had to get a hold of Sony Support--good luck with that! I sure hope you can get a replacement unit...
With the other problems you describe (except for shopping on the Sony Store), it sounds like you had a bum unit to begin with. I've never had problems with my 505 charging via USB--and you should be getting far better battery life than three days! Something like two to three weeks is what you should be able to expect.
I hope you're able to get a replacement that fixes both your screen and your battery issues. It sounds to me like you probably got a lemon of a unit and that could well be why the screen broke after a seemingly inconsequential fall.
Good luck!
dordale