Slow Computer Affects Entire Network?

Can a slow computer actually slow down an entire network?

We have a client who we support remotely. Each of the eight computers in the entire network is used solely for the purpose of data entry and positng to a DOS based program. When one computer on their P2P network recently broke they replaced it with another. Now they claim that the new computer is extremely slow and that when in use it slows down the entire network. Is this possible? The computer by itself didn’t seem slow. Could it be the network card or some network setting?