Got my new celica a couple of weeks back, was a slow struggling start up, obviously I'd never heard it start before but thought I'd eventually get round to finding out the problem, not sure how long it had been doing it in total but done it to me for just over 2 weeks, next really cold night when i tried to start the car and there was nothing.
Luckily had a battery from my old celica that I'd recently charged incase my brother needed it, so changed it over... started up and good as new! So yeah mate, I know you've already decided its your battery but just so you have no hestitation at the counter when your handing over your money
