2008 chevy cobalt lt having issue after issue, but still not fixed.

My timing belt went out about two weeks ago, i had it replaced at the shop for a hefty amount, it started right up after, however it wouldnt start after that initial start, The mechanic said my computer system was fried because when little cars like that have a lot of work done it resets the computer, So i paid to have that replaced, took it home and it ran fine for a few minutes. When i had planned to go do errands, it wouldnt start. if it sat for good few hours, it would then start up, but once you ran it and shut it off, it wouldnt start again. until it was rested, did this for a few days. So i took it back into the shop, they said it was my starter, they replaced that along with my battery cables, i figured all would be fine, but its been now three days and its still doing the same thing. So i;ve replaced my timing belt, started, computer, cables, battery is not even a year old, and have spent a hefty penny on it. What else could be possibly causing this issue of not starting after its ran for awhile?