Buy a new bit of wire? I would do some basic checks on the current bit of wire. It's not the horrible pre-moulded thin stuff is it?
Each end should unscrew, then you can inspect the connection with the core and the screen.
I have to say though your set-up sounds very strange. I have done DIY systems where the aerial comes down to the living room, and then the rest of the house is distributed from an up-link so that the signal can include the VCR output, but never seen that as standard. The presumption therefore is that somebody before you did something similar. In my cases, the "rest of the house" went via an amplifier module hidden away somewhere - any chance you also have one and it's gone wrong?
I can't imagine this would be very hard to sort out if I was there to see for myself - do you have nobody who could help?