Ryan:

First you have to fix the neutral safety switch, since the current for the starter solenoid goes through it. I expect that the screw that holds the switch operating lever to the transmission lever has fallen out, so that the switch itself does not move any more. The back-up lights work off the same switch -- this is why they don't work anymore. Crawl under and check.

If this is the case, vibration can move the switch a bit, and you lose contact, and the starter won't engage.

Rather than guess, you need to get either a multi-meter or a cheap test lamp. Connect one lead to the engine and the other to the starter solenoid connection and operate the key. If you get voltage, the rest of the system is OK and you need to get the starter out and the solenoid replaced. If no voltage, you need to fix the rest of the system.

If the neutral safety switch it buggered, you can bypass it (I don't recommend this, sooner or later you will start the car in gear and hit something). The key switch has also been known to fail, 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!