Below is a post from 2010. I am having the exact same intermittant problem that is almost impossible to make happen for a mechanic.

2001 JGC Limited, V8. The vehicle will not start occasionally, there is no clicking but I heard an odd brushing noise from I think under the dash in the area of the glove box. This usually happens after the vehicle was recently driven. It may be fine for days or weeks and then it occurs again. We have had the starter replaced once. The vehicle will start after a 10-15 minute wait.

Any ideas or help would be appreciated. Thanks.

I have a 2001 Jeep Grand Cherokee Limited with 70,000 miles on it that is suffering from and intermittent start problem. The starter has been replaced 2 times, the positive connector to the starter has been replaced, and the battery has been replaced.

I have tried to understand the intermittent pattern but have been unable to. It sometimes stops behaving poorly for lengthy periods like days or weeks and then comes back with a vengeance. I drove it for about 2 weeks after the starter and cable connector was replaced and it appeared to solve the problem but then the problem reappeared.

This morning it started in my driveway and I drove it to my buddies garage this morning after running it for about 1/2 of an hour, turned it off and immediately tried to start it again, and it started 2 times in a row and the 3rd time it did not start. I left it there for him to continue to try and repair.

At one time I figured it was heat related meaning when then vehicle was hot, it would not start but that has not been the case.

Can anyone help me please? Could this be a computer related problem or a shifter switch related problem? I have fiddled with the shifter but that does not seem to change anything.