So my girlfriend and I recently became owners of a 1985 300D and we are having an issue with the electrical system. When the car is running the glow plug light stays on the whole time. We have driven the car at night with no obvious issues. When I went to start the car today the battery was drained enough that it couldn't get the engine to even turn over. Got it started on the first try with a jump, but as usual the glow plug light stays on. Is there a possibility that the glow plugs are draining the battery even when the car is off? The battery is only a week old.

more likely is that the glow relay is defective and you have a loose pair of alternator belts, or a bad voltage regulator.

ok. pardon my ignorance of the way the alternator works, this is my first car. should the alternator be able to charge a dead battery in idle? should the alternator be able to charge a dead battery with the lights on driving down the highway?

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1985 300D, 112k miles

no. a dead battery will quickly cook an alternator.
especially the measly 45-65A units our cars are saddled with...
but it should be easily able to maintain a fresh battery with every accessory on driving down the highway. the Glow plugs are NOT accessories. if they are indeed on, you'd need at least a 100 amp alternator to keep the battery charged, and run the normal accessories. probably more like 140A...
I'd get a voltmeter out and measure the voltage going to the glow plugs and see if they are indeed energized after 45 seconds have elapsed...
if they are, you can pop the hood, turn on the key, and glow then start the car, then pull the wire harness that feeds the glow plugs. the light should then go out, and if not, at least the glows are not burning out your alternator!

Having the glow plugs on all the time will also shorten their life. Sounds like a new pre-glow relay is in order.

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"Buster" in the '95

Our all-Diesel family
1996 E300D (W210) . .338,000 miles Wife's car
2005 E320 CDI . . 113,000 miles My car
Santa Rosa population 176,762 (2022)
Total. . . . . . . . . . . . 627,762
"Oh lord won't you buy me a Mercedes Benz."
-- Janis Joplin, October 1, 1970

When you are done driving; remove the Plug Relay Plastic Cover and pull off the small Square connector. When you Pull the Connector off listen for any clicking of the Relay. If they Relay clicks when you Pull the Square Connector (remember your Key is off) it means that somehow voltage is still going into the Relay. This could be an Ignition Switch issue.

Pull both of the Connectors off and that will keep the Relay from Killing the Battery overnight.

With the Key off and a Voltmeter see if you are getting any Voltage to any of the wires in that Square Connector.

The writing and the white arrows point to places on the Glow Plug Regulator where you should have Battery Voltage all of the time regardless of the Key position.

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84 300D, 82 Volvo 244Gl Diesel

Just fixed the same problem on my 83 300D A new glow plug relay unit did the trick.

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2012 Mercedes ML350 Bluetec 91K (hers)
2005 Corvette 55K (fun car)
2002 VW Jetta TDI 231K (mine)
1998 Volvo S70 T5 Turbo 196K (kids)
1994 Ford F150 4WD 249K (firewood hauler)
1983 Mercedes 300D 376K (diesel commuter)