Don,
Yes, Avast, or any other antivirus program could potentially be causing a connection issue and therefore creating the error message you are seeing.
You aren't alone ! You'll note that the Avast forums have quite a few problems just like your's. Do a Search for "0x800CCC0E" at the forum search link below:
http://forum.avast.com/index.php?board=;action=search
Please check the links below for possible solutions:
XIMS: Outlook Express POP3, Error 0x800ccc0e, Socket Error 10061
Check this Avast Support link about e-mail difficulties:
avast! 4 changes my POP3 and SMPT settings to 127.0.0.1 and also the names of my e-mail accounts are modified, so I cannot send any messages. What is wrong?
Have you tried disabling the antivirus program, then sending/receiving the mail?
Hope this helps.
Grif
I am using windows me, internet explorer. up to this point I have had no trouble receiving my mail. today I downloaded the free avast virus prevention program. would this program have anything to do with my inability to recieve my e-mail ?. the message I get when attempting to get my mail is "the connection to the server has failed.socket error 10061,error number 0x800CCC0E

Chowhound
Comic Vine
GameFAQs
GameSpot
Giant Bomb
TechRepublic