Well, not that I'm an expert on this, but my '95 Integra died a few times . I think the forum here is slanted more towards the high performance freaks that find this kind of question boring.

There are a few things that can croak to kill your ride like that. For an engine to run you need and engine that can use the crankshaft to turn the camshaft along with spark at the right time and fuel.

Timing belt-when it breaks your car shuts of immediately . If you are lucky you didn't screw up the valves but I don't know that engine. Your car will still make some compression when turning it over so you might have to take off the valve cover to see if its broken.

Coil-when it opens or is out of spec or partially shorting your car won't start or may shut off when it gets hots. There is a simple test you can do with an ohmeter to determine if the coil is good.

Ignitor-mine is OK but I replaced it before I found the bad coil. If the ignitor is bad the car won't start.

Fuel pump relay-if this is bad your fuel pump won't run or it will shut off when the relay gets hot.There are a series of clicks you can hear when you rotate the key before you engage the starter. After one of these clicks the fuel pump should run briefly and then shut off after another click. When your car starts and has oil pressure the relay turns on the fuel pump again.

You can do a few tests to see if some of this stuff is working. Test for spark and fuel pressure. Crank the engine with one of the spark leads off and very close to a ground. Alternatively you can use a spark tester. No spark or weak spark and your car won't run.

You can test for fuel pressure on the side of the road by unscrewing or loosening the little bolt in the fuel filter assembly and seeing if fuel comes flying out when you engage the key. This can be very dangerous if you car engine is hot and do this at your own risk. In a shop they would stick a gauge on there to see if there was pressure.

Another idea is that your kill switch is doing its job and then some