Seen as I don't currently have an electric guitar, I picked up my uncles old classical guitar from the loft. After a while I managed to tune it with a Korg tuner, using the mic.

However when I got round to tuning the 6th string, the machine head was very stiff. There was a click and now the peg turns freely, but the worm gear does not and the the string is now stuck a fair way out of tune.

I thought that the peg and the little rod it is attached to had come out of its little hole, so the peg was turning freely but not moving any other part of the assembley?

Sorry for the hit-and-miss description but I don't currently have a photo, though I can get one at some point if one is needed.

Any help is gladly appreciated.

Maybe the knob broke loose at the end of the shaft thus letting it seem as though you are tuning it but not really turning the shaft?
Maybe one of the gears broke. Check the teeth on the gears
I do sure love me them Gibsons boy