Hi my name is Suzanne.
I have 2 separate Sansa (sold by Ikea) flexible (cable) lighting tracks in my living room. One track works fine, the other does not light. These were here when we purchased the house which is about 4 yrs ago.
I cleaned the cables from dust, all the wires that hold the halogen lights and replaced all the halogen bulbs with the same voltage bulbs. The lights worked for a day or so then when I turn on the switch, they don't work anymore.

The cable connection to electricity go into the wall so I am afraid to try anything different than I have already done.

I thought it was lots of dust and some rusting of the wires, but fixed all that.

What should I trouble shoot next?

Sounds like Low Voltage, Torroid Type transformer likely at Large Connection(Starting Point), If what I am thinking. Each are energized. If 1 fixture works, other should light, unless track is cracked,or broke.
Otherwise, problem at light fixture.
Look carefully at connection point.
Swap Bulbs of good fixture. Also Wipe bulbs clean, fingerprints, contamination, can cause bulb to overheat, and blow.