Dieselfuel12v

This isn't that big of a problem, but it drained my battery in the last week so i'd like to fix it. When the trucks been sitting for a day, it will fire instantly for a second....then die. Then it takes 5+ seconds of cranking to start. It high idles fine, and if you blip the throttle it idles down nicely. It will do this everytime you cold start it. Seems like a fuel delivery problem, where it fires up with the left over gas in the carb, then has to build pressure again?

Side issue that might be related, once in awhile it will start-up with a miss like its only hitting on 3 cyl's, this only happens when its warm.