Headlights won't come on are headlight dimmer switch won't work my low beams and high beams won't come on my 2003 Cadillac DeVille but however the running lights will come on when I put the car in gear and drive my high beam switch doesn't work either

Here is how they are suppose to work .
Headlamps
The headlamps may be turned on two different ways. First, when the driver places the headlamp switch in the HEADLAMP position, for normal operation. Second, with the headlamp switch placed in the OFF position, for automatic lamp control (ALC). During ALC, the headlamps will be in day time running lamp (DRL) operation in daylight conditions, or low beam operation in low light conditions. The LH HDLPand RH HDLP fuses, supply battery positive voltage from the underhood junction block to the left and right headlamps. The circuit continues through both low and high beam lamps, then back to the underhood junction block. The low beam and high beam circuits continue to the headlamp switch. The low beam and high beam circuits also provide the body control module (BCM) with both low and high beam inputs. The headlamp switch includes the dimmer switch and the flash-to-pass switch. When the headlamp switch is placed in the HEADLAMP position a path to ground is provided. Ground is provided at G201. Depending on the position of the high/low beam switch, either the low or high beam circuit will now have power and ground.
The LH HDLP fuse in the underhood junction block, supplies battery positive voltage to the automatic lamp control (ALC) headlamp relay coil circuit. The ALC relay switch circuit is connected to the low beam circuit at the headlamp switch. When the headlamp switch is placed in the OFF position, the BCM will automatically turn on the low beams in low light conditions. The BCM energizes the ALC relay, closing the switch contacts and grounding the low beam circuit. Ground is provided at G201. With the headlights in the low beam position, the high beams may be momentarily turned on or flashed with the dimmer switch handle. The flash-to-pass feature is accomplished by pulling the dimmer switch handle toward the driver. The headlights may be switched to high beam with the opposite movement of the dimmer switch lever. When the headlamp dimmer switch handle is pulled toward the driver, the flash-to-pass switch closes grounding the high beam circuit. Ground is provided at G201. Both high beams will remain on until the driver releases the switch handle.
If the driver places the headlight switch in the HEADLAMP position , the headlights will remain on until turned off or the battery runs dead.

Finding a wiring diagram to use along with a DMM - digital multi-meter (voltmeter ) To test the electrical circuits for the headlamps B+ power & ground side of the circuit is the way to find a fix .
Watching a few basic electrical testing video's on youtube may help you .
Basic Electricity for Service Techs Ohm law Current Flow Opens Shorts
How to Use Multimeter to Troubleshoot Common Problems
The Trainer 18 Electrical Testing Tips
Can take years to learn how to trouble shoot automotive electrical systems properly .

Have you checked to see if the headlight switch and dimmer switch for power on both low and high beam circuits ?

The headlight switch gets power for the headlights from a 50amp fuse.
The fuse powers the headlight switch then the dimmer switch breaks for high and low beams. So if the high beams work, the problem may be with the dimmer switch.
The dimmer switch is made into the turn signal switch on the column. You would need to check the low and high beam circuits at the switch for power.

Headlamps
The headlamps are operated when the driver places the headlamp switch in the HEADLAMP position. The LT HDLP and RT HDLP fuse in the IP fuse block, supply battery positive voltage to both the left and right headlamps. The low beam and high beam circuits continue to the headlamp switch. Depending on the position of the dimmer switch, either the low or high beam circuit will now have a path to ground. Ground is provided at G204. The low beam and high beam circuits also provide the body control module (BCM) with both low and high beam inputs. The headlamp switch includes the dimmer and the flash-to-pass switch.
If the headlight switch is left in the HEADLAMP position, the headlights will remain on until turned off or the battery runs dead.
Daytime Running Lamps (DRL)
Any function that turns on the headlights will cancel the daytime running lamps operation. The LT HDLP fuse in the IP fuse block supplies battery positive voltage to the daytime running lamp (DRL) relay coil circuit. The DRL relay switch contacts are connected to the low beam circuit. When the headlamp switch is placed in the OFF position, the BCM will turn on the daytime running lamps. The BCM energizes the DRL relay, closing the switch contacts and grounding the low beam circuit at G204. The DRL illuminate the low beam headlights at a reduced intensity. The DRL will operate when the ignition switch is in the RUN position, the gear selector is not in the PARK position and the parking brake is released. When these conditions have been met the DRL will illuminate.
DRL operation in Manual Transmission equipped vehicles will occur when the ignition switch is in the RUN position, and the parking brake is released.

Probably the dimmer switch . But without testing that would be just a guess . Turnning the headlamps on Any function that turns on the headlights will cancel the daytime running lamps operation..
No ,don't think the DRL relay has anything to do with it .

View wiring diagrams an testing the electrical circuits at the dimmer switch would be the proper way to diagnose .

No the dimmer switch doesn't change high/low beams just interior lights. Did you try changing the bulbs?

Good Luck,
Subikid90

Classic switch problem. Replace your switch and this will fix your problem.

possibly head lamp switch. daytime running lights on separate circuit and use the high beams at reduced voltage. does flash to pass work? that's high beams too. do high beams work?

Is it just low beams?
do taillights work?

https://s12.postimg.org/6o2zcv3hp/jetta_headlamps.jpg

Click on the link.
This is for 03 jetta gls
There are fuses for left and right low beams. Headlights on low beam, use a test light, see if voltage on fuse circuit? If no voltage that will lead us back to dimmer switch or problem with wiring circuit from dimmer switch.

Ckeck the headlight connections they are notorious for corroding. Check the ground connection for the lights. Pull your dimmer switch back as if you were flashing a car to pass and see if they work there. If they do you have a dimmer switch problem.

probably the connections on the lever/arm .