Old RCX Wires Have Become Grey and Brittle
This is a common issue with the older Lego 9V cables. Lots of sources, including myself, have experienced the same thing - this particular chemistry of insulation ages poorly, no matter how well it's stored. Cables made later, circa 2004-2006 don't seem to have this issue - the insulation is less rubbery and more plasticy, and is still shiny like new to this day.
As far as repairing them goes, it's fairly simple and cheap, albeit a bit tedious. See this reddit thread and this YouTube video. The procedure which worked for me is as follows:

Use a thin flathead screwdriver or knife blade to pry off the back of the connector. There's a little tab that holds it in place.

The inside of the backplate has two ridges for guiding the wire out the back of the connector. Sand/cut these off - you'll need as much space to work with inside the connector as possible. I used a dremel.

The old wires are not soldered to the connectors so they are easy to remove. They are held in place by two tiny forks which are pushed through the insulation to connect the metal inside.

There is a little post in the center of the connector which the wire folded around. Twist it off with some needle-nose pliers.

Cut some 24-gauge speaker cable to size. Does not need to be speaker cable, but most speaker cable I've seen has two leads side by side, like the original RCX cables. You can even use two separate insulated wires if you can't find double wire.

Attach the new wires to the metal contact pads inside the connector. This is the hardest part, because the amount of space inside the connector is very small; remember you have to put the backplate back on when you're done. I could not achieve the sharp fold of the original wires, so don't bother trying. I also could not achieve the solderless connection with the little metal forks - so I soldered the new wires to the pads.
TIPS FOR SOLDERING:

Use high heat and as little time as possible to melt the solder to the wire and contact pad. Applying heat for more than 1-2 seconds will deform the plastic on the top of the connector. No pressure; if you need to add more heat/solder, just make sure the contact pad is cool to the touch before you try again.
I like to ball up the bare wire at the end of the speaker cable and stuff it into the back of one of the metal studs, then melt solder over top.
Don't bridge the gap between the two contact pads!


Once both wires are attached, add a small bead of plastic glue or epoxy on top of the two contact pads and the cable. The glue transfers force from the cable to the connector body instead of to your crappy solder joints.

Reattach the backplate. It should snap into place with a little force, use the screwdriver again if you need to. Mop up any of the glue that squishes out around the backplate - especially make sure the metal contacts on the underside of the connector are clean! Test to make sure it works.


As I said, it's tedious, but this procedure is effective and creates a strong connection between the cable and the connector body. I'm currently repairing about 40-50 wires using this method to get a little more life out of a Mindstorms classroom set.
The RCX light sensors from this era suffer a similar problem because their cables are attached to the sensor body. They can be successfully repaired in a similar way (refer to that YouTube channel I linked).