OK so does the light stay on permanently...not flashing?
Does engine turn over but not fire?
If so then either your chipped key is faulty and you need to take it to the Dealers with proof of ownership of the Jeep for them to supply you with new ones or you have most likely a wiring problem.
If you look at the wiring diagrams for the ASD relay you should be able to see if it is energizing as it should if the chipped key has been recognised by the PCM. In other words both +12 volts and ground must be present on the coil of the ASD relay.
If there is +12 volts on pin 30 (red/yellow) then you need to trace if the wire coming off pin 87 (dark green/orange)is finding its way to the correct pin at the PCM at the PCM...ie. wire not broken, not shorting to ground, not a bad connector in its path and not a dirty pin at the PCM connector....you should be able to find +12 volts right at the wire before it enters the PCM connector.
Wrap a sharp pin or needle around the Red lead of your multi meter and pierce the insulation in the wire just before it enters the PCM to contact the copper wire within...you can seal the insulation afterwards with some glue or melting the insulation with a soldering iron.
If that +12 volts is present there then possibly the PCM or that connector is faulty but as I stated the Jeep cannot be Hot Wired by placing +12 volts there....the PCM has other secret means of stopping the Jeep from firing.
I would start by getting the Dealers to provide you with new programmed keys and if that does not work then the Dealers will need to check out the PCM and SKIM/SKREEM module on top of the steering column....the PCM/ECM is usually a pretty robust component.
What year/model is your Jeep...presume it is 2002 3.7 gasser.
I will look through the wiring diagrams...used to be able to post copies of scanned-in pages from my PC from my Laptop but not sure about that on this revised new site look!
Edit to Add: I am used to the SKIS system on the Diesel models...looking through the wiring diagrams it would seem that the Gassers may work differently as regards the use of the ASD relay. So I need to know if lamp is flashing or is ON solid or flashing so that I can go through the wiring diagrams!
Fuses of interest are Fuse #36 30 A and Fuse #26 15 A in PDC ie. box under the hood.