No, the wireless router will not need to be connected to a PC.
What connection do you have, and what model is your Linksys router?
If you have an ADSL (phone line) connection and your router has a built-in modem like most do these days, then yes you can plug it straight into the phone line and switch it on, and your laptop (assuming you have a wireless adaptor in it) should detect it. Judging from what you said about it coming from a shop, this seems most likely.
If you have a Cable (NTL, Telewest, etc) connection and your setup is similar to what I had in my university house last year, you'll need to plug the router via an ethernet cable into the back of the cable modem, which will have already been installed and connected to the network by your provider - and not into a phone line.
But the short answer to your question, "does it have to be connected to a PC" is no.