Definitely sounds like a bad solenoid -- it's not engaging the starter motor like is should when you try to start (the click) and refusing to stop cranking when you let go of the key is the giveaway -- it stays on when not energized, too!

Could just be the solenoid, may be a sticking drive assembly, too.

Peter

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1972 220D ?? miles
1988 300E 200,012
1987 300D Turbo killed 9/25/07, 275,000 miles
1985 Volvo 740 GLE Turobodiesel 218,000
1972 280 SE 4.5 165, 000 - It runs!