Yes there are actually 4 of those, although only 1 is visible in the picture. Which part is the likely culprit, ie, what should I try first?

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1985 380SE Blue/Blue - 230,000 miles
2012 Subaru Forester 5-speed
2005 Toyota Sienna
2004 Chrysler Sebring convertible
1999 Toyota Tacoma

Rectifiers or diodes very very very seldom are intermittent. They either work or dont.

Yours are the small black pair in pic 1 in the upper left above the transformer.

The large tall black cylinder in the lower left of pic 2 is your filter cap.

"These days known as 1000uF 35V." I concur. You can go larger on either number but smaller is NOT recommended especially on the 35V.

Ebay, radio shack, Mouser ect... should last for at least 10 years of 24/7 use.

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1985 300D 198K sold
1982 300D 202K
1989 300E 125K
1992 940T

"If you dont have time to do it safely, you dont have time to do it"

"The democracy will cease to exist when you take away from those who are willing to work and give to those who would not."

There is a bridge rectifier visible in the lower left of the first pic.
A DC power supply will work through that for the time being, until the diodes fry completely and you are left with an open circuit.
You can buy a universal 18v plug-in power supply that will handle all the transformer and DC conversion duties. Harbor Freight sells one for about $25 that comes with a free crappy cordless drill. Just cut the plug off, and solder the leads onto the board after the bridge rectifier.

Hey it works! The new capacitor is 1/10 the size of the old one - I hope its right. I wasn't sure how the rectifier should be mounted, so I winged it. Got cold solders on the chassis, but theres a common wire to ground separately with a screw. And no more hum! Thanks for all the help.

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1985 380SE Blue/Blue - 230,000 miles
2012 Subaru Forester 5-speed
2005 Toyota Sienna
2004 Chrysler Sebring convertible
1999 Toyota Tacoma

I'm scared! Ha Ha, glad it works. Yeah I figured the new cap would be a lot smaller. Make sure you have the polarity correct. But it would probably be blown already if it wasn't!

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1998 C230 330,000 miles (currently dead of second failed EIS, yours will fail too, turning you into the dealer's personal human cash machine)
1988 F150 144,000 miles (leaks all the colors of the rainbow)
Previous stars: 1981 Brava 210,000 miles, 1978 128 150,000 miles, 1977 B200 Van 175,000 miles, 1972 Vega (great, if rusty, car), 1972 Celica, 1986.5 Supra

I was definitely scared! As you can see I don't solder things for a living. I avoid it because I usually end up screwing up the project and throwing it away. But this time the force was with me.

I got 2 light bulbs that fit, except when I plug them in, the receiver buzzes louder than ever. Maybe there is another cap I need to attack!

__________________
1985 380SE Blue/Blue - 230,000 miles
2012 Subaru Forester 5-speed
2005 Toyota Sienna
2004 Chrysler Sebring convertible
1999 Toyota Tacoma