Do you have "other" power in the car, like wipers/ tail/ park, dome, etc? Heater?
First thing I'd do is pull the connector off the dimmer switch, pull out the headlight switch, and probe all three. You should have power on 1 wire. If so, plug it back in and probe all 3 terminals. You should still have power on the first wire you found it on, as well as a second. When you actuate the switch, that power should switch to the third terminal. Power in from the light switch, power out on either hi or lo beam.
From there power goes through the bulkhead terminals in the connector to the lamps. They have a common ground, near or on the radiator support. Perhaps it is loose/ corroded.