Intermittent starting problems?

My car is a 1997 Hyundai Tiburon with approx 75000 miles on it. It is the smaller engine (I think it's a 1.7L?). The problem is that the car will not start intermittently.

The symptoms are:
car will not start but will crank fine, but either doesn't seem to get enough spark/fire, or doesn't get any.

Unfortunately, the only time it has happened (very intermittently) is when my wife has the car. Every time, it will start eventually, either during the same cranking, or after letting it rest for a moment and then trying again. Today, it took my wife 10 minutes to get it started. She let it crank for a very long time, then had given up. Then 5 minutes or so later, she tried again, again with no results. After 10 minutes she tried again and it started.

To me, it has done this only once or twice, and only briefly. Each time, another try was enough for it to start up ok. With me, it seemed like it was trying to start but didn't have fuel (crank, crank, stumble, crank, crank, stumble, etc.). However, I've never been able to reproduce.

I thought it might be the fuel pump, but it's never had hesitation problems, nor has it ever died during driving - highway or otherwise. I thought that fuel supply problems almost always manifest themselves as both difficulty starting AND stalling at high speeds. I've experienced none of the latter EVER in this car.

If you think it is the fuel pump, why doesn't it do it at speed ever?

Thanks,
Kelly