1999 Honda Accord Engine quits intermittantly

The car qiuts every once in a while. Doesn't really matter what your doing. (At a stop light, excellerating from stop or just cruising along at 55) We recently checked the check engine dash light for any codes and the only code was the cat converter showed so we had that replaced. The dash light went out but the car continues to quit. It was also doing this before the converter was replaced. When it quits you can start it right away but it only runs for about a second, then if you wait about 30 seconds it starts fine and you can go for another 100 miles before it quits again. Any suggestions would be appreciated. I'd rather try fixing it myself, than a shop.