Open the gas cap, have someone turn the ignition key to "Run" but not to "Start."
Listen for a humming or whirring noise from the fuel filler hole. That'll be the fuel pump running to charge the lines. It'll only run for a second.
If you don't hear that-the pump is not working. Check fuel pump fuse at the fuse block inside the car. If fuse is good, check fuel pump wiring connections at the tank (secure). If all looks good-but no pump noise-pump is bad. Involves removing the gas tank, usually.
To check for spark, pull a spark plug wire and stick a phillips-type screwdriver (With a nice, thick plastic handle) into the plug wire boot so it fits somewhat snugly and while keeping one hand in your pocket (so you don't inadvertantly touch any metal on the car-thus making you part of the secondary ignition circuit), hold the shaft of the screwdriver within 1/8" from any exposed metal part of the engine block (avoid fuel lines) while someone attempts to start the car. You should see a fat blue or orange spark jump from the screwdriver to the metal part every time that plug fires.
If one plug is firing-chances are good that they all are firing.
If your fuel pump runs and you have spark at the plugs-it'll run.
Any other computer-related problems will not keep the engine from running-it'll just run badly if something there is not right. but it will be driveable.
If no spark at plug-work backwards from there and check all connections (clean/tight). Check distributor if you have one or coil pack.
Bad primary (low-voltage, small wires) connections will keep the secondary (high voltage, big wires) from working.