Are viruses supposed to just disappear from the virus chest?

I had an incident last week where I couldn’t move the infected files to the chest, but after running a boot scan and multiple other scans, the files didn’t show up any more. Today, when I went to my virus chest, there were three files in it, with names that I had never seen before (they were different from the ones from last week). One was something like win32.exe, the second was the url of a website that I’ve never heard of, and the last one was .dll. I scanned the first two and it said [trj] (I’m assuming that means trojan), but when I tried to scan the last one, I got a blue screen with an error message. My computer restarted and then when I went to check the virus chest again, all three files had disappeared. Also, I keep getting messages from Windows telling me to “turn on Avast!Antivirus.” I’m running scans right now, but so far nothing has turned up. Are viruses supposed to just disappear from the virus chest? And if they aren’t, where did those three files go? Sorry about the long post, I’m just super paranoid about viruses because I don’t have the administrator password so I can’t run any programs.

I'm just super paranoid about viruses because I don't have the administrator password so I can't run any programs.
then who can?

if you want a check inside, this is the guide to follow. http://forum.avast.com/index.php?topic=53253.0
when the requested logs are attached, a removal expert will check for infections