I think I see the issue. I have two iCloud accounts. One for my main Apple ID (app store, etc.) which is a gmail email and is what I'm logged into from my Windows desktop. The second is my me.com email address (which is the address associated with my Facebook account and a second email account that I use). So, on my phone I do have 2 Factor Authentication activated, but that is associated with the gmail iCloud account.
Prior to the change, I could send/receive email from both of these accounts from my Windows Live Mail 2012 on my desktop. Now, the me.com one is not authenticating. I don't know how to activate 2 Factor Authentication on my me.com AppleID since it seems you have to do it from an iOS device and I don't have a Mac or iPad, just my iPhone.
Does that make sense?? Is there a way I can get my me.com working again from my Windows desktop without altering my existing gmail email? Of course both work from my phone.
Thanks in advance!