I'd say that they're ######ed.
Possible reasons:
Ignition has been left on for quite a while with the engine not running
Condenser knackered
Ballast resistor knackered (supplying 12v to the points when it's running)
I'd check the ballast resistor first, just to eliminate it, put a multimeter on the positive terminal on the coil, with the engine running it should show around 6v. If it shows higher than 8v the ballast is knackered.
New points anyway, but change the condenser as well.
Unless of course you're gonna do the electronic ignition swap.