The computer froze on other occasions now when no browser was active and when no internet connection was established (e.g. while the virus scan and the defrag were running).
The computer also freezes frequently while I start it.
Judging from this, I'd say either the computer is just old and that might be a factor, or it's infected with some pretty nasty malware. My suggestion would be to try to boot the computer into safe mode and run a scan then. I'd recommend downloading a couple manual scanners before doing so. I'd go with Malwarebytes and Superantispyware (make sure they were updated with the latest definitions). While I'm not sure how well it'd work, Spybot may also be helpful. These programs will not interfere with your antivirus.
The reason I am suggesting using multiple scanners rather than just one is that using more than one scanner (an antivirus plus some antispyware/antimalware type programs) increases the chances of malware being caught, and these chances are further increased if you are able to scan in safe mode. I'd recommend scanning one at a time though, starting with the antivirus and going onto the other programs. Even if you don't find anything, I'd still recommend scanning at least once with all the scanners.
But if this doesn't work, the only other thing I can suggest, as a last resort, is to reformat.
The free memory line always seems to be near 100% while the CPU seems to be between 40% and 60% most of the time with occasional jabs beyond the 80% (no clue what might cause these). This is while several Firefox windows are up.
I'm not sure what "free memory line" is, but I do know that the more CPU being taken up, the slower the PC will run. If this is happening while there are many Firefox windows open, then I would assume it's Firefox causing the issue here and that closing down Firefox would eliminate the problem. If this problem seems alleviated after you close down Firefox, I would recommend not having so many Firefox windows open. Too many windows open can cause slowdowns (influenced by how much RAM there is and how many processing cores I believe). For instance, a computer with 2 processing cores and 3 GB of RAM would be able to handle having more applications and windows open than a computer with just 1 processing core and 512 MB of RAM.
I would take a look at Task Manager if I were you, to see what program(s) are taking up so much CPU (System Idle Process doesn't count; this is supposed to have high CPU usage). While I'm not sure it'll solve exactly what's wrong with the computer, knowing what programs are taking up so much CPU could be useful, I believe.
