What causes the motor to run fine for 10 or 20 mins then die?

It doesnt start back up untill it's completely cooled down, I changed the spark plugs and the old one which are only a few months old had really bad carbon deposites, before I did it wouldnt start at all, Im thinking its bad gas bu Im not for sure, could it be he ignition coil packs? Or does it sound like bad gas?

Ok that narrows it down, I did two different diagnostics and no code came up at all, whats the best way to check for spark or fuel? If a code doesnt come up does that mean the crank sensor is fine?

Ok, thank you so much for your advice, it does sound like a crank sensor to me but before I assume that I will check the fuel pressure and check for spark, and yes I will definitely let you know what I find out, again thank you

Ok, I did a spark and fuel test, and I found spark to the plugs but theres no fuel coming from the test valve on the motor, not even a little, so does that sound like a fuel pump?

Awesome, thank you, I shall do that and see how it turns out.

I have one more question, some one told me a relay sounds more likely than a pump because he said fuel pumps dont work then not then work then not, but if hes right how could I tell if I have a bad relay? Or do you think hes wrong?

Ok I had another theory, I tried changing out the fuel pump relay which on my car is under the passenger side glove box next on top of the secondary fuse box and it fired right up and ran the whole time but it idled at 2000rpms and didnt go down, then I turned it off and it wouldnt start back up, so does this still sound like a fuel pump problem?

I successfully installed a new fuel pump and that didnt fix the problem, and it gets adequate spark, so the only other thing I can think of is the throttle, what do you think?

Would that indicate a bad icm if no power reached the injectors? And I checked fuel pressure again and the test valve shown no pressure but I disconnected the feed from it and fuel blasted out, but I wanted to hear your opinion before concluding anything, could that mean a bad regulator?

I think I have found the problem, the check engine light did not light up untill the car died again, so right then and there I did a diagnostic, trouble code 58 came up and it said fault with anti-theft system, can you tell me what to star looking at like the module itself or a relay?