When I go to start my car after it's been.

When I go to start my car after it's been sitting for 3-5 hours or more, it just won't fire. After I crank it for anywhere from 20-45 minuets, it fires up, but I have to let it run idle for a bit before I press on the gas at all or it will stall. After that, it runs and drives fine, and as long as it's warm (not sitting for more than 3-5 hours), it'll start rite back up. I've had people tell me it was the fuel pump, and I replaced it. Had a tune up done 6 months ago. Battery and alternator are good, air filter good, and I run lucas fuel system/injector cleaner every 2 weeks when I fill up. I'm baffeled as to what it could be, or as to what I can do to get it started for now, untill I can get it fixed by a pro. Please HELP! Thank you for your time! I look forward to hear your diagnosis.