this actually happened to me in my 83 300D.

The starter got stuck on after a start but it was freezing cold out and I had the heat blower motor on full speed. I never heard it. after about 25 minutes of driving the lights started to dim, and the radio shut off. i pulled over and heard it running. I was able to turn it off by tapping on the solonoid with a stick, but that starter never turned again. upon disassembly, the brushes were shot and had welded themselves to the armature. it was a sad sight. Lesson: make sure everything is OK before firing up the AC or radio on a loud diesel!!!

PS: I completed the final 3000 miles of this trip without shutting the 300D off. As soon as I got home I ordered the starter and had it installed within 3 hours. still running fine, so I suspect it was a defective solonoid, upon removal I found it was a cheap reman.

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Matt
2003 Jetta Wagon TDI 145,000MI
1999.5 Jetta TDI 287,000MI
2001 Suzuki SV650S 26,000MI
2008 Yamaha Vino 125 11,000MI
http://www.crazymatt.org