Why would a DSL connection slow down on the base PC after a wireless router called a Netgear WGR614 is added?

On any wireless connection you can often experience a loss of quality and therefore speed, particulally with high powered uses, like gaming or video streaming, where lost packets are more noticeable (web surfing should probably not be effected). This gets worse as you move further from the router and as the signal has to travel through thick walls. Also, if your router is on or near a large metal surface, eg a radiator, it could help to move it further away. Generally wires offer more consistent and generally faster connections, balanced of course by the convenience of wireless networking.