Wow, that's frustrating. have you determined that the A/C does work? Try moving the temp wheel until it locks to full A/C and see if it cools. Also, cycle the recirc button, the sound of the air flow should change when switched to recirc from normal mode. Maybe your stuck in recirc mode without it being lit up? And I think you said earlier that there wasn't any residue on the inside from a heater core?

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dtf
1994 E320 Wagon (Died @ 308,669 miles)
1995 E300 Diesel (228,000)
1999 E300 Turbodiesel ( died @ 255,000)
2006 Toyota Tundra SR5 AC 4X4 (115,000 miles) rusted frame - sold to chop shop
2011 Audi A4 Avant (165,000 miles) Seized engine - donated to Salvation Army
BMW 330 xi 6 speed manual (175,034 miles)
2014 E350 4Matic Wagon 128,000 miles
2018 Dodge Ram 21,000 miles