I had a problem with my 2002 Branson 3510 fuel pump, fuel lines and bracket that holds fuel filter bowl. My tractor needed help to crank but once cranked up it ran fine. If you shut it down and didn't start it within a day or so it needed help to crank and eventually would not crank.
First, I changed fuel filter and found plastic fuel filter bowl cracked, ordered new parts, changed and bled fuel system, it cranked up and I thought I had success, wrong same thing happening.
Second, I just thought the 12 volt fuel pump was sounding different, it was noticeably louder and within minutes it burned up, the small circuit board was charred. I found the cause it was the fuel lines pinching off, original fuel lines I guess. Replaced all fuel rubber lines except high pressure lines. It still didn't work. (up until this point I had someone helping me that knew what to look for)
Third, I just got lucky...while trying to bled injectors my daughter noticed fuel coming from bracket holding fuel filter bowl. Upon closer inspection the aluminum inlet and exit elbow were loose, I could not twist them but I could wiggle them straight out. I used J. B. Weld to secure them, bled again and success.
My tractor had a series of problems with the fuel delivery system.