My boiler is working but the hot water supply has gone cold.. ?

I have a potterton gas bolier and a Hercal vented cylinder. While the boiler is working (central heating), the hot water supply has gone cold.
There is a thermostat attached to the front of the cylinder and the neon where it plugs in does not light up. The downstairs fuse is ok
There is also a cable coming from the top of the cylinder which has a three pin plug but is not plugged in anywhere.
My questions - could the thermostat have gone bust and would that stop the neon from lighting..and how could this be fixed?
Also, if I plug the cable from the top of the cylinder, would I get hot water in the meanwhile by heating with the immersion rod? thanks