My 1997 Jeep Grand Cherokee does a hard start after sitting alnight or even a few hours. Once it starts and I drive it I have no problems shutting it off and starting it right back up. It's as though it is getting cold. I have replaced the battery, checked the starter.

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Several things could be wrong . Bad TPC or air intake valve or idle air control unit . Check those 3 to start.

Like he said

the starter sounds like ur problem for starting the jeep since u changed the battery the computer really did not have to be changed and for the car only running for a couple hrs u might have a clog in ur fuel filter located by the gas tank under the car very easy to change once u locate it. it doe not sound like ur fuel pump cause the car does run for a couple of hours if it was the fuel pump problem it would not even run for more then 10 mins if that.

It sounds like a bad starter solenoid/starter, because a starter sits so close to a engine and exhaust that over the years the heat starts breaking down the components and when you drive your Jeep the starter solenoid gets "heat soaked" so when you've been driving your Jeep around for awhile and then turn it off the solenoid is "heat soaked", it needs to cool off before it will engage the starter again. Sometimes it can take up to a few hours to work again. Some people hit the starter w(the engine off) with a hammer to try to free it up.

The solution is to replace the starter with a new one and your Jeep will start up every time. Most starters come with a new solenoid already attached so it's best to replace them both.

Your crank sensor might be the culprit that's causing your problem. Have it checked.

crank senor

I had a similar, but not exact, problem and it turned out to be my fuel pump.  About $600 to fix.

It may not be the same problem But, My Jeep would quit until it cooled down and then I could start it and it would run again. Did this on and off for weeks. Turned out that it was the sending unit in the fuel tank. Cold fuel, no problem. warm fuel it would shut off. Cost me $500. Hope this helps, Good Luck

Check the map sensor.