What year is your accord? I had a problem similar to that with mine. If it was too hot inside the car when i got in it to start it, the car would first start and then die, and then keep cranking with nothing happening. Turns out it was the PGM-FI relay under the dash. It is a common problem for fourth and fifth gen accords. If thats what it is, its and easy DIY fix and the part is only like 40 bucks or something.