Why does my car only start after sitting a while?

My car is a 2000 Ford Contour 4 cylinder 2.0 SE

When I go to store and i'm there about ten minutes come back out try to start the car and it will not crank. All dash lights come on, the fuel pump is in gauging and I have no anti theft locking system on this car. After the car sits for a minimum of at least 2 hours the car will start right up.

I have replaced the Ignition tumbler and the Ignition switch but I'm still having the same problem

Two days ago I removed the starter and had it tested and it was fine came home re installed the starter and the car started right up. I drove it around my neighborhood came back to the house shut it off and started it right back up. Then tried it once more and it would not crank. Once again the dash light come on and fuel pump is in gauging.

Other detail:
-I can let the car sit a couple hours then try to start it and the car will run. When the car will not start I try to jump it and it trys to turn over but it just sounds like the battery is extremely dead
-I have tested the battery under a load an it is fine.
-I'm beginning to think I have a short somewhere

Sorry for the vague detail I'm not very mechanically inclined

Clean the battery terminal (both sides of each wire). If there's a relay between the battery switch and starter - replace the relay (very cheap usually) if cleaning up the terminals doesn't work.

If none of the above fixes is it may be just something overheating the starter and causing and electirical open condition (wouldn't be caught in a test as the starter was cold) . Douse the starter with cool water and see if that 'wakes it up' as a test when it is in a fail state.

@Dave & Jennifer Crews I have cleaned the terminals and they are making contact.

@CB I have cleaned the terminals and they are making contact also I'm having trouble finding a fuse panel diagram online since the car did not come with one when I purchased it.

I'll go with the cleaning of the cables and the relay but cold water won't do anything unless you plan on dousing it for a half hour.

I still think that the battery's to blame. If the wires or terminals are corroded you're not going to have proper voltage.

You need to have the battery *load tested at any store that sells new ones other than Auto Zone. A free 15 second load test will tell you the reserve amperage capacity. Amperage spins starter motors not voltage. It takes very few amps to touch-off the lights on the dash. The starter motor on the other-hand requires more battery amperage than every electrical system in the car COMBINED.

A trusted private mechanic or dealer of the car COULD HAVE done a quick battery amperage draw test while it was still bolted to the motor.