1990 Nissan Sentra Intermittent Rough Running with no Gauge

I was idling behind another car for a just a few minutes and my car started running really rough. The engine wasn't responsive to the throttle and my coolant gauge and fuel gauge both went all the way down. The car has 1/2 tank of gas and I had been driving it for about 30 minutes, so it was at operating temperature.

The car eventually died and I pushed it to the side of the road. I tried to restart it, but the starter wouldn't come on. After sitting for 15 minutes while I called a tow truck, I tried it again and it started right up with no problems and I drove 3 miles to my office.

This may be related to the problem above: I did notice that sometimes the ignition switch doesn't engage the starter on the first try, but it always has on the second. I thought that I perhaps had a bad clutch switch or a bad ignition switch.