1. The three system files you refer to, I'm assuming they are in the System Files section of the chest (kernel32.dll, winsock.dll and wsock32.dll) ?
2. If so they are back-ups avast copies of important system files and not infected. The chest is made up od sections and the main one of concern is Infected Files, the name speaks for itself. The User Files section, is for files that you the user thinks are suspect (but undetected) and you can manually add them to the User Files section of the chest.
If 1. above is correct then this also wasn't causing the failure to boot, so I can't see how copying them back (effectively overwriting the originals) had that effect, so it may just have been a computer glitch. However if that is incorrect, yes that could have the effect you mention though there are occasions when malware puts file in the system folders to confuse the user into thinking they were system files.
If by the first time you ran avast, you mean the boot-time scan after the installation, check the C:\Program Files\Alwil Software\Avast4\DATA\report\aswBoot.txt file that should list what was detected.
If you happen to be in this can't boot situation again, you might be able to boot into safe mode, keep pecking away at the F8 key on boot to interrupt the boot, select boot into safe mode. once in safe mode start avast and open the chest, etc. you should be able to report the original file name and location.