I know that under 10.04 you had to go and manually change the mode of the network in the Ubuntu network settings to Ad-hoc, I've not used WiFi on 12.04 but is this the same issue?
UPDATE: OK, I've not got wireless installed on my Ubuntu box just now. However, if you click on the up/down arrow in the info bar at the top of the screen.. Then "Edit Connections" - Wireless. You should have a wireless connection entry in the list. If not, you will need to add one. In the settings box for the wireless connection, the second box down is labelled "Mode". This should be on "Ad-hoc" not on "Infrastructure".
If it is already set to Ad-hoc, make sure that the SSID is correct. If the Band is set to auto, try the correct band for your desktop PC, also check that the Channel is set to the same as your desktop. On the security tab, change the security to match your desktop; Win7 defaults to WPA2-Personal. Make sure that you've entered the key correctly. On the IPv4 tab, try manually setting the IP details. Choose an unused IP address on the same network as your desktop. For example, if the desktop has an IP of 10.0.0.1 associated with the Wireless network, the "mask" will be 255.255.255.0 by default so you must choose an address of 10.0.0.2 - 10.0.0.254, make the gateway the IP address of the desktop (e.g. 10.0.0.1 in this example).