Can a modem be infected?

Out of the clear blue, Windows 7 on my Compaq desktop computer started telling me my password was wrong and would not let me logon.
I carried the fool thing to my sister's house to work on it together as she has a rescue disk for win 7

We followed the directions on http://pcsupport.about.com/od/windows7/ht/reset-password-windows-7.htm and were able to create a new password that worked.

We did a cleanup using ccleaner, atf, Jrt awd and windows own disk cleanup. Everything was good
We scanned with Malwarebytes, Spybot, Eset, MSERT. Found lots of minor stuff (Mindspark, Open Candy, Yontoo, Couponbar, etc) but Spybot also found and cleaned W3i.105.fraud and Malwarebytes found w3i.A. Not sure if these are awful or not.

Working great, so I lugged it home. Connected all the cables and the password once again would not be accepted.
Brought it back to my sister's and no problem with the login password.

What the heck could the issue be????
Any ideas what to check next?

 

Thank you