I have some old ESGE fenders (I suppose that would be SKS now). They are the chromoplastic commuter versions. P55s.

The bike came with a rear light mounted on the rear mudguard and a rear tire-friction side mounted dynamo. The positive current traveled by a wire from the dynamo to where the mudguard attaches to the frame behind the crankset. From there the current travels from through the aluminum side strip inside the mudguard to the rear light.

The mudguard no longer conducts.

If I were to get a new mudguards, would the come with the hardware to connect to an from the aluminum strip in the mudguard? If not, can the hardware be purchased separately?

Pics and more detail are needed.
Have you tried to google, to find info on the mud guards?

My first guess is it's the contacts, not the mudguard. How do you connect the rear light to the conductive strip; a screw goes into the plastic and cuts into the aluminum, or something like that? If so, maybe the screw and/or the aluminum have oxidized a bit... some kind of gentle acid might remove the oxidation enough to reestabish contact. There are conductive glues, which might help... if the glue is waterproof, that is.

The four photos are all of the rear mudguard. The first photo is of the front outside, the second is the front inside, the third is the read inside, and the fourth is the rear outside.

Electricity enters through the connector at the front, and exits to the rear light via the connector at the rear. Between the connectors, the electricity is conducted along one of the aluminum strips in the mud guard. The ground passes from the rear light through the center aluminum strip of the fender to where the fender is attached to the bike frame at the front of the fender.

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Start by checking for continuity. You can do this with a multi-meter. You do not need an expensive one, $10-$15 will get you what you need.

Check continuity from one positive connector to the other. If you get a good reading, check the ground side.

If the continuity test is good, check out the connections on the light housing.

If that is ok, then the generator might be bad. The multi-meter can do a load test up to 10 amps, plenty for a bike dynamo. Get a buddy to crank the pedals, while you test the output voltage / amps.

Under my local conditions, the electrical connection through the fender corrodes out in about a year. From the appearance of your fenders, your weather is not any better than mine. I would not try to fight it, but accept that the connection is not going to work over a long time, and run instead wires under the fender up to the fender strut and then down the strut. It is best to run a ground wire as well, up to the dynamo, because the ground connection through frame is not very reliable.