I run a similar system, with a netgear modem router. My PC is hard wired via ethernet cable, and two other PCs are connected via wireless USB adapters. All PCs connect independantly to the internet via the router. I would doubt that your wireless connected PC is affecting your wired PC. It would seem to be either the cable or the router that is at fault.
If you have another cable, try replacing the existing one to see if that cures the problem. If you have more than one port available try connecting the cable to another port. Finally try using the USB adapter on the wired PC to see if that works. You should then be able to discover what is causing the problem.