My 2000 Chrysler Voyager back up lights stopped working. The fuse and bulbs are good. Where do I start to solve this problem?

Chris, fuse could be down under the dash to the left kind of near where your left knee would be when you are driving or under hood (engine compartment) in the fuse/relay center.
It could also be faulty flasher, wiring, etc
I will post some trouble shooting links for you.
Press the helpful button.
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check fuse for radio and blower

with the head lights off ,and if you step on the brake pedal does the brake lights come on?

Bad crank position sensor causes this. You can verify if computer has stored a code. Replace sensor will solve the problem.

Check brake light switch located near pivot point on brake pedal. Check for power at and through switch.

Check your fuses, and bulbs.

sounds like the fuelpump might of gone bad the frist thing i would do is to have the fuel preasure checked.start there

check the condensor for debris, also check the front blower fan an its resistor, and again check your freon level

The problem you have is a bad clockspring . There's a recall from Chrysler that you can check @ this link http://www.chrysler.com/en/owners/ .
On the right side of the page you can see a link " recalls " , just enter the last 8 #s of the vin and check if the recall still open . If you never did this recall just take it to your local dealer to have them replace the clockspring on your mini van FREE of charge . Hope this help.

hi try the switch thats on the gear box it shold be a 2 wire job if u select reverse and use a multi meter on the switch and it will give a reading if its good