That explains why you can't set it up again. As this looks like a custom setup I can't help much except to keep using the ethernet cable until you learn enough about your gear and find the product manuals for your Cisco and WAP then read each for setup instructions. My bet and it's just a bet is the WAP needs attention or replacement.

As to the mums PC, no PC to date requires an internet connection to fix startup issues. They do need maintenance and repair but to date and over decades not once did I need an internet connection to the dead PC to fix them.