The wires in the ceiling obviously have another end somewhere. Can you find that other end and pull it from there? It may be possible to put a string on the wire, pull it from the end, and then pull a new wire in with the string. It may also be pinched or stapled or otherwise secured such that this would not work.
I'd also look for any junctions, etc. between the ceiling fixture and the fuse panel; there's a reasonable chance the problem is at a connection somewhere and not in the middle of a buried wire.
