The router is not part of your old PC. Whether or not the router is
physically connected (Ethernet) should not matter. Perhaps as a
security measure you configured the router not to broadcast its SSID?
Turn that feature back on.
Assuming you're using Windows WZC to manage your wireless connections,
once you successfully connect to your network it will be added to the
top of the list of "Preferred networks" and you will automatically log
on (if the network is available).
Just make sure that you don't subsequently connect to another wifi
network that's typically within range of your location, or you'll
connect to that one instead (each time a new wifi network connection is
established, WZC adds that network to the TOP of the "Preferred network"
list; you can re-order the list manually, or delete unwanted entries,
but this "feature" can lead to some unexpected results if you're not
careful).
--
Lem MS MVP -- Networking
To the moon and back with 64 Kbits of RAM and 512 Kbits of ROM.
http://en.wikipedia.org/wiki/Apollo_Guidance_Computer