I was in a drive threw the other night and my Camry cut off. It started right back up again but when I got home, it did the same thing, except this time it didn't start again. I recently had the positive battery terminal replaced due to corrosion so I thought this time the problem might be the negative side. I replaced that one as well but still no start. I also checked all the fuses. When I turn the key in the ignition, it sounds like it wants to start but it won't. I'm young and don't know much about car maintenance, but I'm eager to learn. With that being said, I have no idea what else it could be. So if someone could make a list of all the possible causes (starting with the most likely) then I can find the problem through process of elimination. Any help and advice is much appreciated, thank you.
Additional info: 357k mileage, original EVERYTHING. (Except time belt, replaced that almost a year ago.)

 

The engine turns over but does not start?

If so try give the engine a little throttle when cranking, but not too much or it will flood.

Does engine start when cold?

Check for ignition spark when not starting.

Could also be dirty IAC valve or stuck open EGR valve.