Mail will not send, forward, reply, etc.

Question

Hello world,
I've researched and read many support threads but nothing comes close to describing (or solving) this problem a friend has got with her MBP - I hope someone can help.  Basically revealed as a 'sudden change' in expected results when using the Apple Mail app., as follows:
System: Apple Mail app ver. 5.3 , OS X Lion 10.7.5, used with Google mail only (flawlessly for about a year so far on this machine).  No changes or updates were applied (that might be known) so this is a puzzling problem, an nothing else seems to be affected.
In the Mail app, when attempting to Send, Reply, Reply All or Forward a mail message, nothing happens - no message window is presented to allow continuing with the action. This is true whether using the app buttons for these actions, or menu commands or hot-keys.  Mail retrieval continues to be OK; message navigation is not affected, notes can be opened, etc. 
It's obviously not a POP server problem because mail is retrieved OK. SMTP settings all appear to be proper, verified as
Accounts > SMTP server > Advanced:   Use default ports (25,465, 587),  Use SSL.
Possible secondary symptoms?
One first step taken was to ensure all apps were up to date by running Software Update. At the end of the update a restart was required, but was interrupted by the message "Other: Application mail cancelled restart."  Mail was force-closed to proceed with the restart.
After being minimized, the mail window can be reopened from the doc position at bottom right of the desktop, but not by re-selecting the mail app icon in its normal position.  The app bar indicates that Mail has taken focus, but the mail window does not reappear.
After reviewing Mail Preferences and making a minor change, the preferences could not be saved. Instead, the following message appears:   "Error saving preferences.   Writing your preferences to the disk has failed. Your preferences may not have been saved. The permissions on ~/Library/Preferences may be wrong or your disk may be full." I can confirm that the disk is not full; at least 200GB free.
~/Library/Preferences Sharing & Permissions: are found to be: "You can only read / System: Read & Write / wheel: Read only / everyone: Read only
Any help towards resolution is much appreciated.

Answer 1

Thanks, all, for your input.
@~Bee:  Yes, Mail is friendly enough and wll-integrated and probably beats Thunderbird, which is 'Plan B' .  I'm sure this can all be corrected - it's perhaps just a case of finding the straightest path instead of trying 'n' different things and creating 10 other problems along the way.
1.  What do you mean, "sudden change?"  I know you said that no changes were made to the System, but often, changes are made quickly, and forgotten.  So this did not occur after an OS update?
Eseentially: close the lid at night: AOK. Open the lid in the morning: Mail br0k3n.  There was no OS update applied manually other than the after-the-fact update mentioned - and I don't believe anything is running on autopilot.
2.  Please clairify:
the mail window can be reopened from the doc position at bottom right of the desktop, but not by re-selecting the mail app icon in its normal position.
What does "re-selecting the mail app icon in its NORMAL position" mean???
If minimized, the app can be reopened from the minimized app area (stack area) on the right side of the dock. But if you try to reopen by clicking on the original Mail app icon in its original "normal" position in the dock = no action.  My experience is that this is abnormal.
3.  What happens if Mail is opened from the Applications folder?
After this time I can't recall if we tried this or not - I believe so but can't be sure. The Mac is miles away at this time so I may have to relay some things.
Thanks Bee.
PS.  The secret work-around on iOS 6.1.3 battery drain is to turn off Setting > iCloud > Find My <device>