Understood, and apologies for the delay.
So after you unplugged the machine and plugged it back in, mail would open, correct?
In that case.. Lets try this repair next
Open your finder ( magnifying glass ) type in disk utility, and launch the disk utility application.
On the left side of the disk utility window, click your mac hd, then at the upper right hand corner click first aid, then start first aid.
Once it completes. Do this next
Shut down your Mac.
Locate the following keys on the keyboard: Command (⌘), Option, P, and R.
Turn on your Mac.
Press and hold the Command-Option-P-R keys immediately after you hear the startup sound.
Hold these keys until the computer restarts and you hear the startup sound for a second time.
Release the keys.
Then, when the mac starts let me know if its running any better. Or if its still running slow.