you have a short in your alarm system. this will cause your engine to idle ruff and cut off, or, not start at all.
Possible weak battery in the remote.
I had the same problem. Google "keyless entry remote 2003 Jeep Grand Cherokee".
I found a remote for my 1997 Grand Cherokee on Ebay. type in the number "05014736". The remote if for the newer generation Grand Cherokee, but I took it to the dealer, and they programmed it for free.
the dealer does it with a scan tool
replace the remote
There is no such thing as a Cherokee with a 8 cycl unless its a grand Cherokee
No, remote start was not a factory option in 2000.
Check Google.com
Advance auto and Carquest auto parts.
You have to program it with a DRB (Scan tool).
centre top dashboard (red dome)
you have to see a dealer, just went through it an had to pay 80 dollars plus 35dollars for a new remote