Hi,
It is unlikely to be a "Folder".
It is more likely going to be file or files within a folder.
IF Face Time does this in a test Mac User account (or any other Mac User Account you have you could test in)
Then it will most likely be the Files within the Audio File in /Library/Preferences (those settings held for Everyone)
If it only happens in one User Account then the info will be stored in ~/Library/Preferences (The Users Home Folder/Library.
in the User's Own Library/Preferences folder
The com.apple.imagent.plist holds the info for iChat and Face Time whether the Mic is Off or Not
com.apple.imservice.FaceTime.plist hold no info about mIc or volume.
The com.apple.ichat.plist on my iMac holds a reference to a "microphone gain" Setting but I run a AppleScript to change my Audio Settings on Accepting a Video or Audio Invite so I think it is connected to that.
com.apple.audio.AudioMIDISetup.plist can effect the audio in some apps even if you have no MIDI device connected.
This happens when the sample rate is not set to what the app needs or uses.
For Example USB mics should be set to 44100 for iChat to "See" them them whereas the External iSight needs to be at 48000
If your testing seems to limit it to Face Time in any Mac User account on your Mac then it may be the app or an interaction between the App and the System Preferences > Sound settings.
As for Downloading and reinstalling anything from the App Store I have not yet worked that out.
9:20 PM Saturday; December 10, 2011
Please, if posting Logs, do not post any Log info after the line "Binary Images for iChat"
iMac 2.5Ghz 5i 2011 (Lion 10.7.2)
G4/1GhzDual MDD (Leopard 10.5.8)
MacBookPro 2Gb (Snow Leopard 10.6.8)
Mac OS X (10.6.8),
"Limit the Logs to the Bits above Binary Images." No, Seriously