2003 Ford F-150

Is the noise the door ajar warning? Can be either the switch at the claw, or a cracked wire in the rubber conduit the runs from the door, back into the truck.

Try this cure, buy a can of brakekleen and a can of spray white lithium grease, spray the latch area, thats the claw in the door where it closes, spray liberally with brakleen, open and close the door 5-6 times, repeat, then spray with the white lube, open and close the door 5-6 times. Reapeat on all doors.
If the PCM thinks the door is open, none of those things will work.

I am gonna send you to Ford for a scan of B and U codes, something is stored for the door module, or the security module causing the chimes. You will chase this for a long time without a scan, Did you inspect for any broken wires in the door conduit? These B and U codes are not readable with generic scan tools, you will need either a good shop scanner like the Snap on or others in that price range, or pay the 1 hour diagnostic fee at Ford.