I have a toshiba satellite p35-s6053.-LI-ION BATTERY pack model no. pa3385u-1brs (toshiba corporation)part #:psp30u-27w001serial#:95290393k
Batteries no matter it be a lap top or flash light or rechargeable they do go bad if the lap top runs on the power adapter and not when on battery power that is enough info to tell one the battery is shot/gone bad/has a bad cell replace the battery. Rechargeable lap top batteries only have so many charge cycles built into then normally around 2000 and over a three yrs period would emagine the battery has given you this and even more, replace the battery.
Hey Answer Czar; Any compatable battery or adapter will be fine, it doesn't have to be OEM.