If you connect to the router with an ethernet cable, does the computer get its correct 192.168.1.x IP address?
If so, try removing any existing wireless "profile" and then go through the procedure to "Connect" again. In other words, run the wireless adapter's software, scan for "Available Wireless Networks", find and highlight the one that matches your router's SSID (network name) and select the option to "Connect" to it. You should be prompted to enter any WEP or WPA encryption key and, once "Connected", the wireless adapter should get its IP address by DHCP from the router and you should have network and internet access.
If using Windows "Wireless Zero Configuration" to manage your wireless networking (which I'd recommend) then, to Remove the existing "profile" - click here If using third-party software supplied with the adapter, there should be an option within its settings to delete profiles.