Impreza startup problems

I have a '93 Impreza 1.8 L and recently been having trouble with starting it. It starts fine when the engine is cold, but once it is warm and I shut it down for several minutes it doesn't want to start back up. I replaced the starter and selenoid out of ignorance to a solution but it is still acting up. Before I replaced the starter I wouldn't get any sound while attempting to start it, but after replacing the starter I atleast get a single click from the starter so I know power is getting to it. The battery is new. Any ideas on what the problem could be?