Windows 7 Ultimate; AVAST free.
Perplexed…When AVAST performs a full scan - typically once a week - it finds some processes that it identifies as threats. However, you can’t select any of them - clicking the item does nothing - consequently you can do nothing with any of them !!
Depends, it could be imposible to solve a problem thas does not exist anymore.
do note that if the scans results run along the lines ‘error…password protected’ theres no need to worry about it.
it is just that the file is password protected and avast is flagging it as such because avast cannot access the file. it does not know if it is malicious or not.
even if it is really malicious, it is inert because it needs to unpack itself for it to be active. after unpacking itself, avast will scan it with file system shield. thus u will still have maximum security from avast. 
Do you happen to be running a custom scan and have elected to also scan memory ?
The reason I ask is you mention the word processes (avast normally uses this process term when it relates to memory) and the fact that you can’t do anything with them; if it is a detection in memory, that isn’t a physical file so can’t be moved to the chest, etc.
Are you viewing these detections, in the results window ‘directly on completion’ of the scan (e.g. you haven’t closed the scan) and not via the Scan Computer, Scan Logs (historic information) ?
So we will need more information on the detections, a screenshot of the results window would help.