Diagnosing problem with 3-way switches

A light fixture in a 3-way circuit stopped working.
I have (3) 14/2 feeds coming into the light fixture, which I assume to be power, switch-1 and switch-2. I have not touched the 3-way switches.
However I am getting only 60v on the power feed. I am getting 120v when I check between 2 different feeds. When I flip one of the 3-way switches, I get 30v on the power feed.
The wiring is 55 year old BX (armoured). I had some loss of insulation on the feeds inside the box from the heat of the fixture. When I bent the wires out of the box, it started to crumble off.
When I turn off the power and check the resistance of the switch feeds, only 1 of them goes to 0 ohms when I flip the switch. The other always appears open with infinite resistance.
I was hoping to avoid running new wiring, but it sounds like I might have a short outside the light fixture box. Should I start by replacing the 3-way switches?
Any other advice/recommendations appreciated.
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If the insulation is crumbling you must remove the box and cut back the armor a few inches on the cables or replace them. As far as you original problem, the first thing that you have to do is identify each cable. You say you have three- two wire cables in the lighting box- That means you have a feed coming in, a feed going out to something else, and a pair of switch legs going to one of your three way switches. If you open your two switch boxes, you should find one - three wire cable at one and both a three wire and two wire at the other. Once you've got it all exposed and identified, someone here can talk you through reconnecting it

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Do an internet search for a schematic of a three-way switch circuit and the problem should be obvious if the original wiring used the proper color code.
How hard is it going to be to replace the wiring? Crumbling insulation sounds bad.
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