Zerfalling

Hi, first time posting. I checked around to see if there was a thread about what is happening to my jeep and couldn't find one that matched (Sorry if there is!)

I bought my 96 XJ 4.0 Classic with 136,000 miles on it and have put a few thousand on since I purchased it early this summer. The first time I experienced this problem was when I went and filled it up the first time. When I went to turn the jeep on only minutes after turning it off it makes a small humming noise (for about 1 second) near the engine.The dash brake light, check engine and wiper fluid lights come on but the jeep didn't turn over. I tried several more times and eventually it just started like normal. Didn't have this problem again till last night when I was starting it up after being in a gas station for no more than 2 minutes (I left the lights on in the parking lot while i was in there) and the same thing happened except it took 15 minutes for it to finally start this time. All electrical functions work still while this is occurring. Weird. I drove it back to campus 1 mile away and parked the car, left the lights on and shut it off to test it again. I turned the car on only seconds this time after it had been running perfectly fine and it had the same exact problem but after only a couple tries it started. Now this seems to happen every other time I start it and it has me a bit concerned.

Any idea what is happening? Again sorry for the long post and if this is already on the forum, i'll delete it if it is. Lastly here is a pic of my beloved XJ (Have a 3" rough country lift sitting in the garage about to go on to explain the silly sticker)