@shewolfnm,
aack.
Pep boys has gone belly up everywhere but down there...
and the free diagnostic by pimple faced teenage boys is worth what you paid for it.
they put a USED alternator on it? what is the warranty?
I think you shoulda spent $20 on a voltage meter, and figured out what the real problem is.
do you have a test light? ($5)
I can walk you through diagnosing it if you can find a meter...
double aack.
i'd lean toward the starter with the current information, but it won't cause it to die.
push starting your corrolla won't hurt it unless you do something weird and crazy.