There's some basic diagnostics that need to happen BEFORE you can determine what the issue is.
1. Disconnect the plug at the headlight motor. With a wire running from the positive lead on your battery, touch one side or the other of the plug to the motor. DO NOT GROUND THE OTHER CONNECTION. Try one and if nothing happens, try the other. If it opens, switch the wire to the other connector and see if it closes. Do this in the car with everything hooked up. The motor can get screwed up if tested out of the car and although it's been done (including by myself) with no damage, let's not tempt fate.
If the motor works, it's time to try the power.
2. Connect a test light (or multimeter) to one of the terminals at the plug (from the wiring harness) and with the ignition switch in the RUN position (important), turn the light switch ON. If no light, switch to the other terminal. You should have power at one of these terminals. Now switch the connections and turn the light switch OFF. You should have power at that connector.
No power could mean a few things. The relay under the dash sounds like it's making noise, so that means the light switch is functioning. It also means the relay is working. But, no power means the problem is in the wiring and not the motor.
Once you have located where the breakdown is, then and only then can you figure out what to fix. Otherwise, you can just throw parts, time and money at it like everyone else until you get lucky and accidently fix it.