Sounds like your PATS might be acting up, but I would doublecheck your battery and grounds before diving into the PATS system.
First, check and re-check all of your major ground connections (including the ground strap by the driver's side of the engine, low to the ground) to make sure they are solid.
Also, how old is your battery? Factory original? Or a 3 or 4 year replacement battery?
Check the "built-on" date stamped and/or affixed to the battery case.
Have you tried load/bench testing the battery at an auto parts store? IIRC, Autozone and most other car part shops will test batteries for free.
Have you tried using a volt-meter to get a readout of the battery's voltage? If the battery is older and was completely discharged, it might not be able to fully recover, so it might be rendered useless.
FWIW - Probably not a bad idea to invest a few bucks in a battery tender - they are great little gadgets for seldom driven toys parked in the garage...
G'luck!