Once connected, you can check the status of your wireless connection using the following procedure...

Right Click the Wireless Network Icon in the System Tray and select Open Network Connections.

Select your wireless card icon and Double Click it to open the status page...

Here you can view your connection speed and the number of packets sent and received, as well as the duration of your connection and signal strength.

Clicking the Support Tab at the top of the page shows your IP settings...

If you have failed to obtain an IP address you will see this page with IP settings set to 0.0.0.0 or possibly a 169.x.x.x address.
If you have failed to obtain an IP address, check your TCP/IP settings... and if correctly set attempt to Repair the IP settings by clicking the Repair button, or reattempt your wireless connection from scratch...