90 maxima acting funny on start up

I have a 1990 Maxima that did something really weird today. When I went out to get something for lunch, I cranked the car up and it was acting funny like it was close to missing. I turned the car off and it would not start back up. It would crank but it would not turn over. Finally after I left it for about ten minutes, I came back out, figuring that my compressor was going bad and preventing the car from turning over. I took the belt off the compressor and cranked the car up again. This time, it started up but there seemed to be some smoke coming for a very brief second. I drove it and everything seemed fine.
Then, when I was leaving work, I cranked it up and it was stuttering again. This time I didn't turn it off but let it run. Eventually, it stopped and it was running smoothly. I drove it home and turned it off and turned it back on a few times. It didn't do it again. I'm pretty sure that when I get ready to go to work in the morning, it will do it again.
Does anybody know what is going on? It's never done that before. Could it be bad gas? I put some 87 Octane Shell gas in it Saturday night and now this is happening.

Well, it did it again today. This time, I was getting something to eat and I turned the car off to go in. When I came back out to my car, it wouldn't start. So, I let it sit for a few minutes and when I tried to start it, I had to mash the accelerator for it to start.
I'm thinking that it's the possibly the fuel pump or the fuel injectors. I don't have a check engine lights on in the car so how would I be able to find out what's going on?

Check the link below, read thru all pages...

Next problem. I noticed that my temperature was starting to go up and almost run hot. I had no idea what could be the cause of it. If the car was still, the temperature would run up. Once the car started moving again, the temperature would go back down.
Then, I realized that the fans were not running. What's getting me is that sometimes when I crank up the car, the fans would kick on. Now, they aren't coming on at all. What could be the cause of this and how can I fix it? I don't want the car to run hot and blow a head gasket or crack a head. I've been down that road with my Chevy Lumina and it wasn't good.

Check EGR temp sensor, its connector, fan relays... All is controlled from ECU, this means that bad ECU wiring/ connector contacts can cause 'any' problem.

HowTo: see page http://www.cardomain.com/ride/748507/8
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Loose belt, worn pump blades, air in the coolin system may also cause overheating. That may blow the head gasket(s), take care...