If the ethernet problem is that the computer is too far from the router, you could try a pair of Powerline adapters. They allow the signal that usually comes through the ethernet cable to be carried through your home's electricity suppy.
You plug into the nearest socket near the computer and wire the etherrnet cable that comes with it into the PC. Do the same at the router's end and provided they're on the same electric circuit, you should be able to go online.
You can buy them in any PC store or on e-Bay and here in England, they cost around £25 for the pair.