Kinda hard to do if you can't start the jeep to drive it out there lol...If you have a autozone near you might wana have them hook it up to the computer and see if they can find the issue. Worth a check its free.
Because fron 98 and up it does not work in that way .I have the 2001 and turning the key on/off 3 times doesn't do the fancy gauge dance, but if your check engine light is on, it will display error codes.
I actually had an alarm system on mine and it wouldn not even turn over if the system was armed. Nothing at all when the key turned.Ok, start simple.
Do you have an alarm system? If so, it may be stopping you from starting the engine, but usually if that's the case it will at least turn over, just not start.
Also, it's not in drive is it? Or in gear?
Did you do anything else besides replace the battery? How long was it sitting with a dead battery? What was the problem that led you to believe the battery was dead to begin with?