It's been my experience that when the Diagnostic Socket doesn't light up, the OVP relay needs to be replaced. The good news is that they are cheap so cheap that you should order two new ones at the same time. I have had new ones fail right out of the box. This is highly unlikely with two and if one happens to fail, send it back but you'll still be able to solve your problem.

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03 CLK430 Cabrio 211K Pweter Silver/ Oyster Leather
90 300SEL 214k Pearl Black/ Alto Grey/Black Leather

Prior: 85 190E, 88 300TE, 89 300TE, 90 300E 2.6, 90 300TE, 92 300E 2.6, 91 and 93 300SL, 87 Ferrari Mondial Cabrio

Update:
I disconnected the battery and took the OVP relay out this week. After bench testing in, taking the case off and poking around, I put it back in the car. NO MORE CHECK ENGINE LIGHT. But it couldn't keep itself alive when cold.
For whatever reason, the next day it was just fine. Starts and idles cold, no lights, and strangely the exhaust sounds different (??)
The little LED still doesnt work, but since the CEL is out, I dont care.
-Happy camper

Sorry to say that eventually your CEL will return. When you disconnect the battery, the CEL system turns off until your car has completed 6-8 duty cycles (cold engine to normal operating temp, back to cold engine= 1 duty cycle). BTW this is the way to solve a failed smog test due to the CEL being on. After the needed duty cycles have been completed, unless you have repaired what was wrong, the CEL will come back on.

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03 CLK430 Cabrio 211K Pweter Silver/ Oyster Leather
90 300SEL 214k Pearl Black/ Alto Grey/Black Leather

Prior: 85 190E, 88 300TE, 89 300TE, 90 300E 2.6, 90 300TE, 92 300E 2.6, 91 and 93 300SL, 87 Ferrari Mondial Cabrio