Did you delete LW's preferences folder? It's a good idea to do that after upgrading

Make sure that the XP firewall is off & that the PC Tools firewall is configured to allow LW.

Did you have LW on the laptop before you bought Pro? Did you always see the firewall icon & do you see if on the desktop?

If you can find the model of the router, we might be able to find instructions for port forwarding.

A few people had weird connection issues with an earlier Java update (1.6.0_01)...are you using Java 6 u 2 on the desktop? I'm using the latest update & it's fine for me, but if you like you can try installing this older Java on the laptop...if it makes no difference then you can always reinstall 6 update 2 again. Use the JRE offline installer & remove your current Java version before you install this one.
Archive: Download Java 2 Platform Standard Edition (J2SE) 5.0 Update 11