Assuming you've got rear discs, not drums (since you're talking about calipers), the handbrake actually acts on a small drum brake built into the rear discs, not on the calipers. Since it was only the parking brake that failed the test, the calipers are probably fine.
As for what's causing the problem, I'm not so sure. If the handbrake cables and the brake adjusters are set properly (handbrake pulls up about 5 clicks or so) then the brake mechanism on one or both sides has probably seized. This shouldn't be too much bother to fix - just take the discs off and overhaul the mechanism. Actually, it could just be that one of the handbrake cables has seized.
Anyway, I wouldn't have thought the fix would be too expensive.