Display alternates between dark and bright

Question

I have several issues but I suspect somehow they are all related as they all began about the same time, within about an hour of each other, which was maybe a week ago.
Periodically, my display slowly cycles between dark and bright.  Sometimes the display will suddenly go to sleep on it's own, usually after a period of about 20 seconds of me not doing something and when I wake it up the display is quite dim.  Other times the computer goes to sleep (not just the display) requiring me to log back on.  I use password for startup.  I open the display settings after log-on and the brightness slider has somehow moved way over to the dark end (left).  I slide it up to where I like it and soon it does it again all by itself again after a very short period of inactivity.  I have noticed that if I leave the brightness control alone (dim) without readjusting it it seems to take longer for the other issues to develop.  I would normally place the brightness slider just under half way up.  My sleep time settings are currently: computer - 1 hr, display 15 min.  That is plugged in which is pretty much the only way I ever seem to use it ... plugged in.
Another issue is an occaisional rapid beeping.  It's the same low beep that you hear when you try to do something stupid and the computer is telling you you've made an error.  The difference is this is a long, unending string of rapid beeps; I'd estimate maybe 15 - 20 beeps per second.  The sound does not stop.  I have to mute the speakers to shut it up.  I have not yet been able to determine a recognizable pattern of common variables for when this happens.  The other day when the computer went to sleep by itself and I woke it and tried to input my password and I saw that the input bar was filled with black balls as if it was remembering my password which I did not like but when I hit enter the logon dilaog box shook, the entry field emptied and refilled on it's own.  I held the backspace key for several seconds and nothing seemed to happen.  I used shift/command/arrow to highlight the entire string and deleted it but as soon as the characters were deleted I saw the input line quickly fill back up again one ball at a time at roughly the same rate as the beeps.  Then it occured to me that the beeps were similar to those you would hear if you held a key down and filled an entire entry field with a hundred of a particular character and was still holding down the key long after the field was full.  My first thought was that a key was stuck down.  Not so.  Each and every key is free to move and functions normally.
Last night I closed the lid to put the computer to put it sleep before I went to bed.  About 3 hours later I was awakened by the sound of the rapid beeping.  I got out of bed and went to the computer and opened the lid to find the same input line black balls issue but this time it was accompanied by the beeping and the display was also cycling between bright and dim.  As it was the middle of the night I killed the machine by holding down the power button and forcing a shutdown.  This evening I decided to do the upgrade from 10.9.1 to 10.9.2 hoping that might help but it did not.  I have not heard the beeping since the upgrade but the display is still cycling, which was the first thing I noticed when all of this began.

Answer 1

Turns out it may have been sofware issue.  I suspected software anyway because rebooting could temporarily cure it.  I spoke to an Apple Service and Support person on the phone.  She went through a fairly lengthy process with me to evaluate the machine and determine if it was hardware or software related.   The results of those steps did not lead her to any concrete conclusions but she was able to hear the beeping issue happening in real time.   She guided me through the steps of O/S recovery and now several hours later the machine appears to be functioning as it is supposed to.  Typically the issue(s) would show up after maybe twenty minutes or a half hour after a hard boot.  I am to monitor the thing for the next week or so watching for any signs of the issues slowly returning. 
Here's keeping my fingers crossed.