2003 Hyundai Elantra Won't Start

I have a manual 2003 Hyundai Elantra GT. I had been driving around for an hour or so, and when I was at a red light today and accidentally stalled out. When I tried to restart the car, it would turn over, occasionally sputter, but never catch. After a few minutes of trying, it started and I got back home. A few hours later, I went back out, and this time the car refused to start at all. It turns over fine, but never catches. Any ideas what might be causing this?

Was the engine hot both times it refused to start?  If so I suspect the coil or at least something in the spark system.  

One way of checking this is to buy one new spark plug.  Carry the plug with you and the next time it does not start, get out and pull one plug wire off (pull on the socket part not the wire) put the new plug on that wire and hold the threads of the plug tight against the engine block while you have someone try to start the car.  You should see a bright blue spark, and if you are not holding the plug with an insulated tool, you will also see stars!  This can rule out a spark problem.

Thanks so much! The first time, the engine was hot, and the second time, it had been sitting, but was still a little warm to the touch. The engine runs smoothly when it does start, so it’s very confusing. The only other thing I can think of is that I got a new radio put in at best buy a week ago, and perhaps they screwed with something somewhere.