1996 Vw Passat GLS 2.8L; When I turn the engine off the fan keeps running and is draning the battery? What needs to be looked at?

The snapped belt has a number mark.

How To Install Replace Engine Serpentine Belt Volkswagen ...

? 6:09
https://www.youtube.com/watch?v=urBVruIk348
Dec 31, 2011 - Uploaded by 1A Auto Parts
How To Install Replace Engine Serpentine Belt Volkswagen Beetle 1AAuto.com ... Well, the serpentine belt on my Bugbroke. And, didnt know ...

Help! Serpentine belt broke, need advice. - TDIClub Forums

https://forums.tdiclub.com/showthread.php?t=323672

Jul 11, 2011 - Basically, I think the serpentine belt blew on her, she drove about 1/8 ...TDI(s): 2005 Passat Wagon, 2004 Jetta,99.5 Golf ... BTW, last year I lost my AC belt rather abruptly. .... 2005 VW Passat GLS TDI (Chipped, BSM delete, and Manual ), 2007 VW Eos 2.0T, 2002 Mazda MPV ES, 2015 Toyota Sienna XLE. 1.6 tdi alternator belt tensioner bolt snapped
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VWVortex.com - Broken timing belt, valves likely bent

forums.vwvortex.com > ... > Golf IV & Jetta IV

1. Check the scan data for engine temperature to see if it shows that the engine is running hot. The ECM will turn the A/C relay off if it thinks that the engine is overheating. Check engine coolant temp sensor

2. Test voltage at the Powertrain Control Module (PCM) pin 50 (Yellow) and pin 58 Yellow/Black. Both should have battery voltage when the system is turned on and the engine is running. If not, then the wiring needs to be checked.

3. If battery voltage is present on the two pins, then manually ground pin 68 (Orange) at the PCM and this should ground the A/C relay and the clutch should engage.

4. If it does, verify that the PCM powers and grounds and connections are good.

Take it in to a auto electric shop to be check out,

I know that on the earlier model VW's there was an underhood thermostatic switch for the electric fans. This switch would keep the fans running until the underhood temperature reached a desired level. If this switch were to go bad, it would most definitely cause the problem that you are describing.

Sounds like temp sensor that controls fan is faulty.This would cause fan to stay on all the time or not turn on at all.

You can take it to any mechanic shop that deal with VW.

in a mk3 vw this could be the fan control module thats bust. is the fan spinning at high or low speed?

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Good Luck

check starter motor

Like to make sure that your post says your car is a 1996 with only 38800 miles.
There were many recalls for your vehicle back then which may be the cause of your hard shifting. Are you the original owner ? If so, have you done any scheduled maintenance to it from the day you purchased it ?

https://www.youtube.com/watch?v=qL9V3fJT6QQ

Hope this helps