I just bought this V8 Dakota SLT with 150,000 miles. Ran perfect for 2 months, Here is the problem, Two weeks ago I went to start it and battery was dead. Replaced the battery, two days later the battery was dead. Long story short, the fuel pump was running all he time, I removed the fuel pump relay, and it kept running, I hit the tank, and it quit. So for a week I would remove the fuel pump fuse every time I parked it. Today I went to start it and the battery was dead, I listened and the fuel pump was running, (WITH THE FUSE OUT). What would cause the fuel pump to continue to run.

 

Sounds like the wires are shorting out and making the pump bypass the relay/fuse. Check all wires.

 

I checked the wires, and the wireing harness was pinched between the plastic gas tank seam and the frame. Problem solved. Thanks, Crazy4x4