If the car's location is colder climates, if it was me and it died, I'd give it a full trickle re-charge, as a short term fix.

With the price of a battery being relatively cheap, and an easy replace, I'd put a new battery in as a no-brainer.

If your car stays in warm climates all of the time, you can probably stay with a re-charge, but I would have it tested under load.

Nothing would **** me off more, than getting stuck with a no-start because of a friggin battery.

As far as the TPMS, it's most likely battery related, being it reset under full power...