I would double check the pin outputs and make sure the grounds and hots for one channel are not changed. From what you described it does not sound like a tone arm wiring issue. Not all manufacturers use the same pin out arrangements top to bottom.

I have never had a bad cartridge, but that is not to say it cannot happen. I have had issues with head shell adaptors specifically on Duals with their funky headshell arrangement on their older models.

Good luck.

Depending on how long "long" is, if the cartridge sat for several years, there is a chance the rubber suspension of the stylus assembly has deteriorated and the cantilever isn't responding properly within the field of the magnets. Letting cartridges sit for years is like letting a car sit for years. All the rubber parts begin to either harden or fall apart. If you have a powerful magnifying glass, you can visually check for cracks, though that probably isn't what has happened. The suspension probably hardened and you are unlikely to see this by a visual check. There is really no way to try to soften the suspension without risking permanent damage to the cartridge's internal parts.

That the cartridge made sound in both channels once would indicate it might not be too late to salvage the cartridge for short term use. Without installing the cartridge on the arm, just connect the cartridge leads to the Ortofon and gently, very gently, move the cantilever side to side and up and down slightly. If you cannot get the cartridge to produce a signal out of one channel, and you are certain the tonearm wiring is good, then there is nothing left but to replace the stylus assembly. Replacement is not a bad idea anyway. You can upgrade to a better stylus. Not replacing the stylus assembly soon risks the suspenion collapsing completely and the stylus, without any flexibility of movement, then becomes a literal chisel in your spinning record groove. At that point, a valuable LP could be permanently damaged. Ever seen a lathe in action?

It could also be in the wiring IN the turntable. Try wiring up the catridge backwards (Right pins to left wires, Left pins to right wires) and see if the problem switches sides or not. If you get sound out of the same speaker than it could be a problem with the wiring inside the TT. You could also mount another cartridge on the table and see if you only get one channel as well. If this cartridge works on other 'tables my first instinct is to say that the problem probably isn't in the cartridge, but elsewhere.

Yes, just lightly touch the stylus tip with your finger. There's no need to wear gloves but keep the volume control at a low level. Replacing the stylus assembly on an OM cartridge is quite simple. If you can replace a Christmas tree light, you can replace a stylus.