2003 Dodge Ram where do i start

I have a 2003 dodge ram, 4 door, 2 wheel drive. The truck has been running fine not any issues, except about a month ago on 2 different occasions when i was leaving the house i put it in reverse and it started vibrating pretty bad, i thought it might have been cause of the really cold weather we have been having because after it warmed up it was fine. now i went to get in it and it turns over fine and sounds like it is trying to get fuel but it just wont start. I got some ideas but im an electrician not a mechanic. do you have any suggestions on where to start without dropping the gas tank first. Thank you for your time....

sparky