Thanks. I've learnt something today: Gmail doesn't care much what you enter for the server name.
However, you'll note that the error message you quoted in your original post gives the port as 993, which is the standard port for secured IMAP. That won't work with POP3. You'll note that the port for the working account is shown in your screenshot as 995, which is the standard port for secured POP3.
If you had allowed Windows Live Mail to apply the default settings when setting up these accounts, they would have been configured to use IMAP, connecting to imap.gmail.com over port 993. If you have a good reason to use POP3 instead, then you should connect to pop.gmail.com over port 995.
To get the broken account to work for incoming mail, then, change the server name to pop.gmail.com and the server port for incoming mail to 995.
If you're not able to send with this account, we'd have to see the error message generated when you try to send.