Could be one of the temp sensors has gone bad. Try unplugging the engine coolant temp sensor. On my OM606 (95 E300D), it's blue/green and located in the front of the valve cover by the radiator hose. With the car running, unplug it and see if the fans run.

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RIP:
2011 E350 BlueTEC, Schwartz 81k (totaled by uninsured drunk driver)
1964 Unimog 404.1 (wrongfully towed by the city)
1994 E320, Brilliantsilber 208k (transmission shuffled off after sudden catastrophic fluid loss)
1982 300D, Silberblau under a blue repaint 256k (sold for parts)
1995 E320 Polarweiss, 131k (sold for parts)
1995 E300D Polarweiss, 287k (totaled by drunk driver)