Do you hear the fuel pump? Does it crank? Try wiggling the shifter as you crank. Should start in Park and Neutral. I would remove and clean the engine grounds before replacing anything as that alone can keep things from working. Thanks go to CCken for the pics as thats where i got them.

 

Did you pull a plug to verify spark?

 

 

 

Remove the spark plugs and wire from one spark plugs. Remove the spark plug. Reattach the wire. Touch the bare metal of the spark plug to the engine block to ground it. Hold the wire or use pliers to hold the wire in that position so that the plug is touching the block. Have someone crank the engine (attempt to start the Jeep). If the spark plug Sparks, then you have spark at the cylinders. If it doesn't and you for sure had the plug fully in the wire and fully grounded to the block, then you don't have spark. You can search YouTube for videos.

 

While you are testing for spark test for pump priming as suggested. Have the assistant put the ignition to on (not to start). You should be crouched by the fuel tank listening for the quick whine of the fuel pump priming pressure in the fuel rail. It should go for about two seconds. Then once you hear that move to the front and ground your plug as the assistant cranks the engine moving the ignition from on to start.

 

 

That is - you have no spark - while the assistant is cranking the engine over? The on position primes the fuel pump. The start position of the ignition cranks the starter and sends voltage to the coil.
If you have no spark - but the starter cranks - then test in backwards order from the spark plugs. Check the resistivity in the wires. Check the cap of the distributor for wear. Visually verify that the rotor has plenty of flex for a good connection. Check the wire to the coil for resistivity. Check the coil. Use a manual or try YouTube.
The starter won't have anything to do with a no spark situation. Also, 15 minutes is nothing for an engine to cool. The heat has to pass from the coolant thru the block of the engine. There is no water pump creating a flow to circulate the coolant either. The radiator isn't a part of the equation then either.
When I had an overheating once replacing the crank position sensor was the solution, but that might not be your problem. Do you have a Haynes, Chilton, or factory service manual? Your local library might have other manuals or database to give you wiring diagrams and testing processes to follow.

 

I think cruiser's site has the 99 FSM.
www.cruiser54.com - technical manuals link on the left.

It will have a ton of info for testing in a no spark situation.