I had the same issue the 98 Jeep Grand Cherokee was sitting for some time and did not have the time to get to it, I got it going after a couple of days ago. Here are the steps I went thru.
1) charged the battery to read above 12.6v, checked the voltage across the terminal while running, voltage was dropping below 12v , it should read above 13.5v
2) checked the wires that come out from the alternator, there are four
a) green, green with brown and a black ground wire that come out from the black box or what Chrysler call in the schematic "generator"
b) green and green/brown strip wires go to the PCM
c)at the top of the alternator there is a red (I think it's a gaug 4 wire) that goes and connects outside the fuse box next to the batters, this is the fuseable link, 1/2 red the other 1/2 green. Then there is another thick G4 red wire that connect to the fusable link outside fuse box that goes to the positive terminal.