I did a quick search on that error code and came up with about 8600 different sites on the Internet explaining the cause of this error and how to fix it. I'm rather surprised Belkin couldn't manage to find any of them.
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Here is Microsoft's Knowledgebase article on the subject:
Socket Error 10061 on MS KB
A good site with several different possible causes and resolutions to the problem is:
ProperSupport
This document on Symantec's site gives a more detailed explanation of the problem as well as several fixes. Click on the + next to "Error message always happens when sending or receiving email" about halfway down the page for additional information.
Essentially, you are probably getting this error because of one of two things.
1) The server is rejecting your connection, either because of improper settings, incorrect account name or password, or invalid security settings.
2) Your local firewall, either on the computer or on the router, is blocking access to port 25 for the laptop. This can be caused ether by the firewall specifically blocking this port, or by the router not giving you correct access to the Internet. (Are you able to get to normal web sites on the laptop, or are those failing as well?) If you have Norton Internet Security, download the latest updates as a recent (bad) update was also causing this same problem. If your firewall was previously configured to allow MSIN (Outlook Express) access through the old Linksys adapter, it might need to be told to allow access through the Belkin adapter now. I'm not sure on some firewall software, but Norton Internet Security is very specific when configuring which ports and applications are allowed access on each individual network adapter/connection.