My friends bought the 2Wire 2700 HG-B Wireless Router (with a built in dsl modem) from ebay. Using the internet connection with this has been absolutely disastrous. The internet connection ...

A wireless home network needs a connection to the web (the modem) and wireless access to that connection for your devices (the router). That doesn't mean that you need two separate devices, though.

A modem connects your home network to the internet, and a router lets your devices talk to one another and use that internet connection. Most people need both.