97 Corolla (sometimes) won't start

I don’t know if you still are having this issue or if it has been resolved. Anyway, I too have this problem - exact same thing. I replaced the battery. Problem seemed fixed for 9 months. It resurfaced. I bought a starter thinking for sure this was the problem, however, when I removed the battery cables, I noticed corrosion on the positive terminal. I cleaned, reconnected, and the car started up fine. I ran for 3 months with no issues. Now, the problem is back. This time, I am going to verify the battery is ok under load. I am going to replace the battery terminals and clean corrosion there. I should have done this before, but regrettably did not. I do not think the starter is the problem as it starts fine when a disconnect and reconnect the battery cables. Weird problem. It must be corrosion on the connectors.