If I sign in to a virus free computer with a facebook account that has been hacked, does it become infected?

[Kelsey]

My parents have recently had a virus take over their facebook accounts and they want to change their password, but the virus also moved from their facebook accounts to their computer so they can't change their passwords successfully. If I sign into their facebook accounts on a computer that dosen't have a virus, will it become infected?

I'm sorry I really know nothing about viruses especially these new facebook ones.
Okay thanks, both my parents swear they just clicked on their "messages" folder and then the computer started freaking out. It turned out to be those stupid link messages that sends out links to everyone else on facebook trying to get them to click on it. Ever since then the computer has been a mess.