Re: 94 Grand Cherokee Limited won't start/alarm goes off
Who did your "tuneup"? Did you do it yourself, or take it to a "local garage"? What kind of key are you using, does it have the encoder inside?
With out knowing anything else, I would check that the battery is connected to the alternator, and check that the alternator is good. I would do a total reset, disconnect the battery, pull the IOD fuses in the engine compartment, turn the inginition "on" and drain the IOD capacitors, and turn "off". Then reconnect everything, turn the ignition back "on" the entire system should resest itself.
But honestly, your issue sounds like the Jeep is not recognizing the key, and the vehicle thinks you are trying to steal it. I am suprised the seller did not provide a coded key. There is a small ESD chip inbedded into the coded key, to tell the vehicle that it is the correct key. You may have to go to the "stealer" to purchase a coded key. Or you can purchase the key online, and have the them program it to your vehicle.
I had a problem with a door pin grounding out randomly on my old ZJ, the alarm would blast in the middle of the night. To turn off the alarm with a coded key, open the passenger door with the coded key. This will deactivate the alarm once triggered. The passenger door is the closest to the computer.