I just had the heat soak issue with a starter, thats pretty easy to figure out. Everything should work normally as long as the car is starting from cold, start and run without any issues. But if you drive it for more than 15-20 minutes you won't be able to start it at all.
If the starter is weak all the time then there may be a couple of issues. The starter may be bad and dumping the battery with all the resistance, or you may have a loose cable somewhere (check your grounds). If you've got an extra person you can check the resistance when your cranking it over, if its bad you'll probably spike a couple hundred ohms...
It sounds like your engine is turning over, which probably rules out a hydro-lock. If the cylinders are full of fuel nothing should move at all. Plus you would see that the plugs are wet when you checked for spark. If it is though you'll need to change your oil out before you run it again, as the fuel will leak past the rings into the sump and dilute out all your oil.