OK, I have a 97 4-door, and I can jump start it, and it runs OK, but as soon as I shut it off, and try to restart, no-go.

It has a new battery.  Is there a separate voltage regulator, or is it built into the alternator?

I believe it is on the alt. I had a similar problem with my Sport. The alt was caked in mud and would not charge. I removed it and cleaned it very good. It worked fine after that. It is on the bottom passenger side of the motor I believe.

Are you sure that's a charge problem?

A new battery or even a fully charged good battery should be able to start an engine several times without any recharging - so even with a dead alternator, if the battery is good, you should be able to start it several times in a row before the battery becomes sufficiently discharged.

Does it crank the engine when you try after switching it off?

There are a couple of different things you can try - get a voltmeter and connect it across the battery terminals and then start the engine - jump start it if necessary.  Note the voltage readings before & after starting - if the battery is good, the before reading should be around 12V, and the after reading should be 1~2 volts higher if the alternator is working.

A before reading less than 12V suggests either a defective or discharged battery and an after reading the same as or lower than the before reading would indicate a defective alternator.

You can also charge the battery fully on an external charger and then try starting - it should start half a dozen times in a row with out any issues.