I'll assume that you're having problems with the OEM fog lamp circuit and none of the other circuits that might be described as "running lights". That was the reason for my question (unanswered) in my earlier post.
Don't waste your time looking at the fuses in the Junction Block (the door at the left end of the instrument panel). There are no fuses in the Junction Block that have anything to do with forward lighting.
Your model year 2001 Ram uses switched ground in the fog lamp circuit. There should always be +12 volts present at the base of each bulb, even with everything turned off. That's the red/orange tracer wire at each bulb socket.
Check Fuse G in the Power Distribution Center (under the hood, aft of the driver's-side battery). If you don't have a meter, swap it with another 15 A. fuse (Fuse F should work).
Make certain that the high-beams are not selected. Turn on the headlamps and pull the headlamp switch handle out to the fog-lamps-on position.
If the fog lamps don't light, try swapping the fog lamp relay (also in the Power Distribution Center) with any neighboring relay. See if the lamps light.
If you've gotten this far without success, you have one of the following problems:
Both bulbs burned out.
Defective headlamp switch.
Defective wiring.
Good luck!