Can connecting another computer to my network influence the connections of the other computers?

I had two computers both connected to a wireless router. Yesterday I connected a third computer to the network and, although the connection goes through for this new computer, one of the original computers now says “Limited or no connectivity” and cannot connect to the Internet. Is it possible that the new computer is using up too much bandwidth and is therefore preventing the other computer from accessing the Internet?

Tagged as: bandwidth, computer one, new computer, two computers, wireless router