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Ok, it is going to depend on what the computer are doing.

In short as I understand,

You have internet coming in to a LInksys Wireless router with one PC connected on ethernet and the other on wireless.

Questions.

Which one runs slow?

You should not need a switch to improve preformance, though it is true wireless is slower then the ethernet, the wireless G is many times faster then most consumer broadband internet providers.

If everything is going well on one computer and you turn on the other and things decrease, it seems to me that one computer has something going on that is pulling your bandwidth. I would start my search there looking for the cause of the slow down.