Wireless router connection?

I work in a small office. We have three desktops and one laptop. We currently have a DSL modem from AT&T and a wireless router. The modem is hooked up to one desktop and the router is in a separate room because it has to reach downstairs. We just bought a new router from Cisco, and it would only work if we had it connected to the PC that is connected to the modem. I want to have the router in the room where the old router was. Why won't the router work when it isn't connected to the PC that is connected to the modem? Does a wireless router have to be connected to a PC? I know that it has to be connected to the modem, and it was, but it still wasn't working. Please explain to me why it isn't working. The plainer the English, the better as I am not exactly a computer whiz. Thanks for your help!