Hi, Scott..
In answer to your questions..
1) What was your previous antivirus? How was it removed? - It may be necessary to use the relevant uninstaller
My previous antivirus, and the only antivirus I have used on this computer, is Avast Home. I removed it through the control panel, in the same place you prompted me to do a repair. I removed Avast, restarted, installed Avast, restarted. Was having the problem, before then, and having the problem after.
2) Is ashQuick.exe in C:\Program Files\Alwil Software\Avast4 ? What happens if you run it?
ashQuick.exe is in the program file, yes. When I run it, the scanner that I have been expecting to come up does come up, hesitates for a second (presumably, because I only ran it, and didn't tell it what to scan?), and closes. Just like I have been looking for.
In answer to the first (not numbered) question that you asked.. When you scan something, do you see ashQuick.exe in task manager? No. It does not appear in the task manager. Which might be the problem, the context menu item might just be broken? I don't know..
Not a question, but.. 3) It may be necessary to try a repair of avast!
I followed the instructions that you suggested, it told me "The product was successfully updated", but it did not fix the problem. Even after a restart (had to try it) it didn't bring up the quick scanner.
Thank you for your assistance, and I hope this helps.
Editing to Add: I've never gotten the "Final statistics for the last scan" screen (second picture) when I was done with a context menu scan.