We're only seeing the Wired connection, not the wireless information in the IPconfig output. Which makes sense if you posted from the desktop. Now what I want you to do is the exact same thing on your laptop. Plug it in, then run ipconfig /all and post the results again.
After you've done that, we're going to go through this in sections.
Section 1 - Network Connections
-Open up the control panel and go into the Network Connections folder.
-You should see 2-3 connections: 1394 Connection (maybe), Local Area Connection, and Wireless Network Connection
-NONE of these should be disabled, and none of them should be Bridged (if you expand the status column, it will say Bridged there if it has been).
-If any are disabled, enable them. If any are bridged, deleted the bridges.
-Screenshot and post your network connections folder.
Section 2 - Wireless Network Connection
-Right-click on Wireless Network Connection and select "properties"
-Double click on Internet Protocal (TCP/IP)
-Everything should be set to automatic. If not, change it now.
-Click on the Wireless networks tab.
-Click View Wireless networks. If any are visible, your wireless card is definitely working. If it doesn't detect any, then it is possible it isn't working, or is disabled (which you should have corrected in section 1 already), or the router isn't broadcasting.
-If you do see a wireless network there (any wireless network, not just yours) try to connect to it. In point of fact, screenshot and post that window. If you connect to your network, problem solved. If you can connect to any other network but can't see yours, the problem lies on the router end. HOWEVER - remember, after a hardware reset your router will be returned to its default name and configuration, so you won't see the name you've assigned but rather something generic (like the router name).
As you said you uninstalled and reinstalled the wireless card, it may also have the wrong drivers, but we'll rule this out first.
Follow the steps, post the things I've told you to post, and we'll go from there.
God this would be easier if I could just spend 10 minutes with your computer and router =)