I don't think that the radio working without the key in is unusual. Both my '94 and '99 do that. They are also on a timer so they turn off after about 30 minutes or so if undisturbed. I could be wrong (my wife says that happens a lot).

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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