Originally Posted by csnow

I had the same exact problem with molten connector plugs.
Headlights go dim. Wiggle the connector, and they brighten again, at least for a while.
These things are incredibly weak from the factory.
I should have snapped a picture.
Check the connectors on any other car and compare how much more beefy the terminals are. Very unusual for MB to have under-built components like this. My car even has stock bulbs. High-wattage bulbs would melt them for sure.

Easy fix! Autozone and NAPA both sell replacement 9004 connectors. I used the Autozone ones because they were in stock, and found they are much beefier than the MB ones.
I think they were around $4 each. I suggest soldering them on, and sealing the soldered joints with heat-shrink tubing.

This is how I did it:
1) Remove factory connector from bulb base.
2) Note the position of each wire in the factory connector by its color. I drew a little sketch.
3) Cut wires where they come out of factory connector.
4) Strip wire ends 1/2 inch.
5) Cut 1 inch strips of heat-shrink, and slide one onto each wire on the new connector (away from the soldering area).
6) Twist new connector wires onto factory wires, being careful to match them up correctly, and fold flat.
7) Solder the wire joint.
8) Slide the heat shrink tubing over the wire joint, and shrink (I use one of those fire-starter butane lighters for this step).
9) Put a small dab of grease on each terminal, just for good measure, reassemble, ...and let there be light!

Best of luck.