Why wont the running lights work in a 92 dodge Dakota?

Check the top three:

Bad fuse

Bad light bulbs

And if those check out OK, then check for bad wires to the lights.

Chances are good that the DRL module is toast (Daytime Running Light). This is located on the right hand side of the engine as your looking from the front of the truck. Located on the right fender near the windshield washer tank. The module is about $125.00 ~ $150.00, cheaper from a wrecking yard. Now there could be a few things to keep in mind, emergency brake must be off, vehicle in gear and moved a few feet this should trigger the module, the lights should come on once the truck moves a few feet. Yeah I know....but they set this one up to get a signal from the speedometer to activate the Daytime running lights....so it needs to move before the DRL module gets the signal from the speedometer. Check the fuses in the black box on the same fender, the DRL fuse lives in there, not under the dash.