I have had a 1997 Acura Integra for almost 4 years now and it has never given me any problems, I perform regular maintenance on it and never really drove it too hard. About a month ago I was driving it and I blew a tire, changed it and drove it home where I parked it. I left it sitting for approx. 3-4 days and when I came back out to start it - it wouldn't. I could hear the fuel pump priming and the engine would turn over but not fire. Tried this numerous times and about 3 days of trying, it just started (idle was a bit weak but other than it ran) I left it overnight and it still started no problems the next morning. I drove it to a friend's house to do some work on it and when I tried to start it again it wouldn't. Then a few days later it started again but it sounded like it was choking, it had no power (can't get RPMs past 4000), it blows thick smoke, and it will stall when you try to idle it. Any Ideas? We have not checked the spark plugs yet - however we changed the plug wires, distributor cap, the rotor, and the coil and after that it wouldn't start all together.
When it does not start right away, check the spark at the plugs and determine if there is spark and if it is strong. I assume that the vehicle is getting fuel but it might not be getting all that it needs or more than it needs. Start with the spark and then you might want to have a fuel pressure check done.