1975 Cadillac EL Dorado running rough

This car is a work in progress and I'm learning quite a bit going along. Sometimes it has the tendency to backfire, this morning pulling into work it backfired and a weird noise came from the engine bay. Well this afternoon starting it up the first crank sounded dry (99.9% of the time the first try will sound like it wants to turn over, then the 2nd try it turns over) well it started up the 2nd try but it was running rough. I slowly pressed the accelerator and it died. I started it up again, popped the hood and thought to maybe clean the carburetor would help. It didn't. So I decided to leave, I put it in reverse and it died. I started it up again, got it backed out of my spot and drove home. The entire time driving home there was a delay whenever I pressed the accelerator and it was running rough. Got it home and parked. Did some research and I think it jumped time when it backfired this morning. What do you guys think?

edit: someone informed me that this car does not have a timing belt, rather a pushrod