Having done a bit of research on your problem i think your problem is the Node Type set to Peer-peer which you will see in the ipconfig you posted, on your desktop and on all 2 of my machines including my lappy this is set to hybrid, i've read this setting set to peer-peer it can cause problems connecting to other machines. What OS you using, vista?
Edit:
Peer-Peer Node Type
Node type "Peer-Peer", more appropriately called "Point-Point", is a problem on most small LANs. That means MyComputer requires a WINS server to resolve names. No WINS server means no name resolution, no access to its shared resources, and the dreaded "Name Not Found" error (among various symptoms).
Microsoft has documented (KB903267): a fix for this. You'll need to run the Registry Editor on MyComputer. You need to find the key [HKEY_LOCAL_MACHINE \SYSTEM \CurrentControlSet \Services \NetBT \Parameters], and delete these two values (which ever is there):
* NodeType
* DhcpNodeType
After restarting the computer, rerun IPConfig and examine the results.
If you set the SSID's the same then the computers will automatically connect to which ever wireless router has the strongest signal if you move to a different room with your lappy in stead of you having to manually disconnect and reconnect like you'd have to do if you have different SSID's.