Recently I fixed the temperature display in my 400E, before I had the same problem as yours, blank screen but backlight was OK.
I located the temperature sensor behind the front license plate, I cut the wire and removed the sensor, I measured the resistance of the sensor with multimeter, it showed only 5 ohm, I knew it should be 3k ohm at normal temperature, then I cut the rubber seal and carefully removed the sensor from the metal probe, and measured resistance again, this time it showed around 3K ohm!! guess what? the sensor stuck too deep into the probe, and reached the end of the metal probe, it got short-circuited.
I then put the sensor in, and kept some distance from the tip the probe, and seal the probe with some RTV sealant and let it dry, then bound it with some electric tape, soldered the wire and reattached the probe on the car, I got the display back since then.
I don't know where the sensor locates on your S500, if you can locate the sensor, maybe you can give it a try.
99 BMW 540i 6-speed 110K Km
03 SAAB 9-5 wagon 80K Km
92 400E (Sold) 245K km
Still missing the days with the Benz, it kept me busy.