if it wont turn on with the battery out and the AC plugged in then it aint the battery, most likely is either the charging circuit on the mobo, or the adapter, what happens when you go into the BIOS or can you?
PS. if you had it on hibernate then the battery shouldnt have drained..hibernate turns off the computer where as standby keeps it on....I leave mine in the case for weeks at a time and when I turn it on its still at 100%....I hardly use mine at all, right now I am on a big 17 inch HP Laptop, got mine since July '09 and probably have about 10hrs on it....still have the cover that it ships with covering the screen..talk about pristine condition
If you can get into the BIOS, check the SSD
settings, if it says 0gb then the SSD
is toast, I have read many cases when the battery goes to zero, it seems to kill the SSD