Another starting prob

Ok, i have a 96 cherokee sport, which most of the time will start fine. It's when I start it and dont drive far before i turn it off, it wont start back up without letting it sit. Today i go out to leave, start it up, drive a couple blocks to the store to get cigs, had to turn off jeep since line in store was long, come out, wont start. hours later, started, but idle was weak, and about a block down the road it died and wouldnt start. Gave it 10-15 mins, started up. It doesn't take many cranks to fire when does work. I have new duralast gold battery, new terminals, etc etc. When it isnt starting, i get no "click" or anything, but I do hear fuel pump and everything come on.
I know a lot of threads ask basically the same question, but mine is odd as it starts fine the first time, and after long drives, but if u start it for a minute, shut it off, it wont crank. I would just go through replacing things, but I jus got laid off from work, so money has to be budgeted. If anyone has any ideas and/or links to other threads with this specific problem I would much much much appreciate it. Ive been fixing odd's and ends since the day i transferred this thing into my name. The jeep came from my stepfather who passed, so i refuse to quit dumping time and money in it, it's here to stay. Thank you all for your time and knowledge!

edit: I have tried starting in other gears, didn't help. I did notice my stepfather has removed the cover to the steering column, but i cant really ask for the reasoning behind this. The light around the ignition stays on also, but i assumed that was from the broken hinges and the driver side door bout to fall off, but not sure :\

If the problem is that the starter won't crank then it could be the starter itself, or something upstream from the starter. Force the problem to occur, then crawl under the passenger side of the jeep with a multimeter set to read voltage. Find the starter and put the positive lead on the small center post of the starter solenoid, put the negative lead on a good ground, and have a helper turn the key. If you get voltage to the starter solenoid then the problem is with the solenoid or the starter motor. Otherwise the problem is upstream, perhaps the nuetral safety switch (NSS) or the starter relay etc.

See, I have seen that in many other threads, just since my was different and only did it after SHORT drives, I thought perhaps something else was going on. I will clean the NSS tomorrow, but my reverse lights and such have always worked, and starting in a different gear did nothing, so i assumed the nss would be ok. So yea, ill run through the lists others have posted in the past. Sorry for maybe making the same thread as others, I just honestly thought it would be something different.

Thanks a million though

Do the test described above it will tell you a lot