Yes, the second PC connects wirelessly to the router. The primary PC connects via a cable.
What concerns me is that I previously altered something in the network settings (primary PC). Before this I could just switch the router on and the wireless PC could connect to the internet. Now I need to enable the connection on the primary PC first, for the secondary PC to connect. (maybe it doesn't automatically pick up the ip address)
When reinstalling the primary PC, I'm concerned that I won't be able to connect to the internet on the secondary PC, as I won't be able to enable it.