It sounds like the laser in the MKIII unit is shot. Your options are probably limited to buying new disk reader/laser mechanism or buying a replacement MKIII and dump the one you have (or sell it for parts). Option #1 is not very easy or cheap. There are a few folks who have done this, but it is really only cost-effective if you have a MKIV, in which the replacement cost of the entire unit is much higher than the replacement cost of a MKIII.

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SOLD
2000 E38 750iL Highline Edition, Upgraded with the lastest 2006 X5 Electronics
MKIV Navigation, 16:9 Display, Bluetooth, TV/Video with Backup Camera, Sirius, and Aux Input