Verify/repair the startup disk (not just permissions), as described here:
The Repair functions of Disk Utility: what's it all about?
Go to
Apple Menu > System Preferences > Network, choose
Network Port Configurations from the
Show popup menu, and make sure that the configuration used to connect to Internet appears at the top of the list. Leave checked (enabled) only the port configuration needed to connect to Internet and Built-in Ethernet (in that order if not the same), uncheck (disable) the rest of network port configurations and see whether that helps — if it doesn’t, turn ON again the ones you want enabled.
How many mail accounts do you have in
Mail > Preferences > Accounts and what type are they (POP, IMAP, .Mac)?
In Mail, open
Window > Activity Viewer. What do you see there when Mail refuses to quit? Actually, you may be able to avoid having to force quit Mail by canceling whatever it’s doing (by clicking on the red stop icon of the activity).
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Do you have any Mail plug-ins? In the Finder, go to each of the following folders (if they exist). What do you see there?
/Library/InputManagers/
/Library/Mail/Bundles/
~/Library/InputManagers/
~/Library/Mail/Bundles/
To make accurately reporting that information easier, open
/Applications/Utilities/Terminal, type the following command (you can just copy it here and paste it in Terminal), and press <Return>. You can then copy the output of that command from Terminal and paste it in your reply to this post:
ls -1 /Library/InputManagers /Library/Mail/Bundles ~/Library/InputManagers ~/Library/Mail/Bundles
Note: For those not familiarized with the ~/ notation, it refers to the user’s home folder. You can easily locate any of the folders referred to in this post by copying the folder path here, doing Go > Go to Folder in the Finder, and pasting the folder path there.