ok, I am guessing you are talking about an 89 XJ?
When you shut the key off in a RENIX-II system (like after driving a while or whatever), the ECU holds it's own power on for a little bit (about 2 seconds), during this time the ECU stores some running condition info, and sends pulses to the IAC to "OPEN" the idle passage so that there will be airflow into the intake manifold for your next attempt at starting. Without that airflow... you'll have a tough time starting and maintaining some level of initial idle... The ECU uses the B+ Latch relay in the relay cluster on the passenger's fenderwell to hold on the power after key off The B+ Latch relay is the 3rd relay in that line of relays if you count the one closest to the silver starter relay as #1 (you can swap it with #4 if your AC works to test it)
Map sensor, on the firewall. I think you can just unplug it to see if it starts and runs.
coolant sensor - below the maifolds - it's the one with the "normal" connector (that goofy-connector is on the Knock sensor)... leaving it unplugged will give you like a -40*F start-map... It's worth a try.