1995 Honda Civic LX: Engine shuts off randomly while driving?

Has shut off twice on me for no apparent reason, each time I have pulled to the side of the road and spent about 5 minutes turning the key/engine over without it starting. Lights and radio all working while I'm trying to start the engine so doesn't seem to be the battery. When I'm turning the key the engine and battery lights come on (also right when the car dies) then once the car starts again they turn off. I have had trouble a handful of times in the past few weeks starting my car, the same sequence happens, turn engine over a couple times, lights come on, but eventually starts. Just in the last two days (when I didn't have trouble starting engine at all) did the engine shut off on me after about 15 minutes of driving.

Anyone with tips, or ideas as to what on earth this is would be greatly appreciated! I'm a Uni student with limited funds to keep putting into this car, but I love it, so must treat her right.

Top two suspects are the ignition switch and the Ignition Control Module, also called the Igniter. The trouble starting can also be a bad fuel pump relay, a.k.a. "main relay," but I bet it is the same thing that is killing the car when you are driving, something rare for the main relay.

You can check the warning lights when the engine shuts off. If the warning lights do not come on (particularly oil and battery) you can be sure you have a bad ignition switch. But the timing - 15 minutes on, 5 minutes off, are classic for a failing ICM - in which case the "off" times will increase soon. You can also pull a plug wire and check the spark (helper is very handy) when it is working. The spark should be energetic and have only traces of orange, if any. If it is orange with more pop than snap the ICM goes to the top of the list for sure. You mention your funds are very tight; an ICM from a wrecking yard distributor is satisfactory