Um, what do you mean by on-off switch? On the MX, the on-off switch, so to speak, is the film rewind lever, but even if it is not half-out a normal meter works while the shutter is half-depressed.
Anyway, it could be as simple as the wire to the LEDs breaking or being jarred loose.
There's a service manual for the MX available at
Pentax Manuals. It has diagrams of where the various components of the meter circuits go, so you can play at a (very superficially "potential") diagnosis even without necessarily disassembling the camera, just by correlating things to the external appearance of your camera...