Starting problems

Try checking the battery terminals for a good, clean connection.

Years ago I had a TR-3. One night it was running good; I stopped for 5 minutes; it wouldn't restart with the symptons you described.

Because a battery terminal was loose, it would conduct enough electricy for the lights, etc. But not enough amp.S to turn the starter motor.

However, if that's the problem, you should hear the solinod clicking in and out.

Try checking the cable to the starter motor.

If the problem doesn't lie with the starter/solenoid, it could be the ignition switch or a relay.
My parents had a minivan that would do that very same thing now and then. Shorting the starter would activate it and start the van, but the ignition did nothing but turn on everything else. Turned out to be the ignition switch.
That last turn of the key, that kicks on the starter, wasn't doing a thing. A new ignition switch fixed it up.

With luck, it will be something simple like what I've mentioned, or even better such as what the previous poster mentioned. But if your not so lucky, it could get more tricky.
I don't know much about it, but there are other things that could cause it that you wouldn't think of right off the bat. For example, a switch that tells the car that you are in park. Working correctly, it lets you start the car. But if it thinks the car is in gear when it isn't, you'd turn the key but the starter wouldn't kick in, just as if you really were trying to start the car in Drive or reverse.

Lets hope it's someting simple. :)