What you *could* do is take it over to an AutoZone (or other *helpful* parts store near you) and they can hook the pos/neg up to a battery or one of their battery machines and they can test it for you.
To get it as hot as it would normally, they should only have to fire it a few times and let some electrical heat build up. If the guy knows what he's doing, he'll be able to tell you for sure whether it's good or not.
Then, if it is bad, you can typically pick up a "rebuilt" starter right there on the spot. Then go bolt the new one back in & you're good to go!!
Now, I don't know the Corolla engine compartment, so if the starter is a *behotch* to get out, then this is all easier said than done!!