I had 18 viruses on my work computer and programs and even video games showed on my hard drive that I've never played sites I'd not looked at showing open all day?? Can a virus or maleware cause this?
Yes, it can. Once it gets/bypasses the user account control.
When you are not careful enough while installing something then you might invite a malware inside. Once you have given permission (User Account Control permissions) to run a software that contains malware, then officially you are granting rights to it.
Now you opening a program or the malware opening a program wouldn't make much of a difference to the os since you both posses same rights.
It is quite easy for any malware to do whatever they want. So opening programs are just a child play for a malware. Imagine what will happen if a keylogger is installed and tracks all your keypress, gathers your sensitive information like bank account passwords and passing it outside. Horrible right? One solution could be doing a clean sweep with a good antivirus software and keeping it updated.
Bottomline: Always know what you are installing.