Hi guys, I am very sorry for the delayed response. I thought I had subscribed to the thread, but did not. I never saw your responses.
Here is the resolution: As most of you suggested, the LCD died on me and I replaced it. The original part number is 1265420227. The part number search points to here:
OUTBOARD TEMPERATURE INDICATOR. Fits: Mercedes | Mercedes-Benz of South Atlanta. It does not list the 300SDL, but that is the right part. A different search takes me
here, which indicates that the product is no longer available, but gives you the new part number. Either way, you can get it there for a handsome $525 as of this writing.
I got it here for $30 including shipping:
Mercedes W126 560SEC 500SEC 350SD Outside Digital Temperature Disp Monitor | eBay
So sorry I did not see your post JamesDean, or I would have pinged you first.