2007 pontiac windshield wipers stopped working and you can hear the motor still runs

Check Fuse 29, but by rights, it also covers the washer.

Buick Rendezvous (2002-2007) fuses and relays

https://fuse-box.info > buick > buick-rendezvous-2002-...
Fuse box diagram - Fuse Box Location. It is located in the passenger's side of the center console near the floor, behind the cover.

Buick Rendezvous (2006 - 2007) - fuse box diagram - Auto ...

https://www.autogenius.info > buick-rendezvous-2006-...
Jan 18, 2017 - The floor console fuse block is located to the left of the glove box near the floor. Buick Rendezvous - fuse box - floor console ...

If that fuse is okay. try giving the wiper motor a jolt by whacking it end on with a broom handle. Can you hear the wiper motor running? Check the linkages.

Others have the same issue

https://www.google.com/search?q=2007+Buick+Rendezvous+CXL+wipers+not+working

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test and check -switch-relay-motor-linkage

In the under hood fuse box , should have diagram inside the lid . Front wiper's or rear ? Front fuse # 36 - 25 amp. Plus Two relay's PCB hi and Wiper PCB relay . Wouldn't think this being fuse problem . Wiper switch , motor etc... The wiper's are control by a computer . BCM - body control module .

The windshield wiper/washer system consists of front and rear wipers. The front and rear wipers are operative when the vehicle is in accessory or run. The front wipers have 4 different modes: Mist, Intermittent, Low, and High. When the front wipers are in the intermittent mode, there are 5 delay modes to chose from, commanded by the windshield wiper washer switch through the body control module (BCM). The rear wipers has an only one mode.

If the fuse is bad , could have a short to ground or wiper motor pulling to much current (amps) . Fuse's don't just blow for no reason ! Could also have DTC'S - diagnostic trouble codes stored in the BCM .
DTC B3715
DTC B3873
DTC B3875
DTC B3922

DTC B3715 02: Front Wiper Relay Drive Circuit Short to Ground
The body control module (BCM) controls the wiper motor based on input from the windshield wiper washer switch. The BCM monitors the wiper washer switch through three separate signal circuits and a ground circuit. The windshield wiper switch high signal circuit is used to determine high speed wiper operation, the windshield wiper switch low signal is used to determine low speed, intermittent, and mist operation through the use of a resistor ladder, and windshield washer switch signal circuit is used to determine washer operation.
The BCM controls the windshield wiper motor through two output controls, controlling two different PCB relays which control the desired wiper speed, high or low.
DTC B3922 00: Front Wiper Function Select Circuit

The PCB relay's are non- servicable , replace fuse box . Soldered in Your best bet mit be to take it to a qualified repair shop .

If the wipers are consistent in where they stop the problem may be due to the splined shaft of the drive motor has rotated within wiper linkage attachment. Remove motor/linkage assembly remove linkage from motor and check for stripped splines on the linkage/motor. Willie

I had to run a new ground wire from my wiper motor to a chassis ground to eliminate a similar problem on mine. Mine kept intermittently stopping, of course always at the worst time. The ground wire resolved the issue.

Does the wiper motor run? If you can hear the wiper motor run, the wipers arms may have disconnected from the wiper motor,you will have to remove the wiper arms,and the plastic cover to access the wiper motor,and check for damaged parts.If your wiper motor does nothing at all, you probably blew a fuse do to the resistance on the arms,refer to your owners guide for fuse panel, and fuse locations. hope this helps

You don't have a clue do you ? The wiper motor is controlled by relay's . The wiper switch is a low voltage input to the BCM ,on the voltage signal it see's from the switch it energize's the wiper an wiper high relay's . The relay's are of the PCB type . Which means it's soldered directly to the under hood fuse box circuit board . It's not even hooked to the BCM

the wiper needs to be tighten some more, there is a nut that holds the wiper to the motor tight that nut.

its gotta be shorting out somewhere in the wireing

If the wipers were buried under snow/ice or frozen to the windshield, you may have blown the red 10 amp fuse located in cavity 9 in the fuse block located on the bottom left side of the instrument panel near the parking brake pedal.
In order of easiest to check:
1) ensure wipers not frozen to windshield.
2) ensure wiper arms are not loose on the pivot stud,
3) check the red 10 amp fuse.
You stated that "you can hear the motor". Which motor do you hear? The engine or the wiper motor?
If you hear the wiper motor, then the fuse is alright. Try 1) and 2) above.
PT Stanley