Well, that's a tough one and I can't give you an answer. The tip is heated with RF energy, the base is basically a transmitter. The tip is not heated with DC like other irons.
My cable tester checks for continuity AND RF leakage. I bad cable can still have continuity but the damaged braid is leaking enough RF that the damaged spot gets warm or even hot, although frequently the iron still works... just not well.
However, I will measure my known good one and post back on at least that. I suspect resistance varies by type of tip. The cable however, is just a thin but 100% braid shield coax. So It should read near 0 ohm ground to ground and inner conductor to inner conductor. Easier said than done on the hand piece if you don't have a special test wand to stick in it.
It's likely the base.... you could try to open it and just flip the hidden switch from broken to fixed!
If that doesn't work... check the FET.
I'll post back with resistance on my hand piece and tip in a few when I go to the shop. That info may benefit someone in the future.