Ok, so what is happening is that the circuit for the computer, dash lights, and fuel pump are all getting power when the truck is off. When you look under the dash, do you see any issues that might explain that?
For example, does it look like water has leaked down from the windshield and behind the fusebox? If so, the corrosion may have shorted two wires together (I've had this happen twice with old cars).
Alternately, do you see any "funny" wiring? I would assume the mechanic would have found that, but I mean any wires going into the fusebox that don't appear to belong there? I am thinking like one of those wire tap things that folks use to wire in additional accessories.
Speaking of which, do you have any accessories, like fog lights or an amp? If so, pull the wires and be sure they are not back-feeding the system somehow.
Can you think of any changes that you made at the same time when this problem started? You mention the starter, perhaps the solenoid is bad and is leaking power back into the system? The easy test is to remove the 12v+ wire to the starter solenoid and see what happens.