How do you know if the computer in your car is bad?

I have a 93 Ford Probe and Im having all kinds of problems with it. I will be driving down the road and it will completely die. When I push the gas it wont go anywhere and then it will shut off. It wont crank again until after it's been sitting a while. I thought it was my alternator first so I went and had it tested at auto zone and it was bad so I got a new one hoping this would fix my problem but only a few hours after the new one got put in it started doing the same thing. Now everyone is telling me my computer might be fried. How can you tell if that's it? A new one is around $300 and I don't want to buy one if I don't have to. PLEASE HELP ME!