Cannot boot from recovery, yet hardware diagnostics finds no problem

Question

Hello,
I have a mid-2011 MacBook Air 11" which is running Mountain Lion, with most recent updates.  No new software recently installed, and I was running Pages and a few other standards apps, when....
suddenly, computer started just going black and restarting, then would work for 10-30 seconds, then go black and restart.
It has been like this for two days, and now almost never even gets to the login screen.  Usually, it just goes black after the Apple icon and starts over, sometimes the cursor appears in the upper left on that screen as well (which seems bizarre).  Sometimes it will load the linen background, with the cursor in the upper left hand corner, but then be totally frozen.
Here's what I've tried:
-Ran the apple hardware diagnostics by holding "D" on startup.  Both normal test and extensive test revealed no problems.
-Tried command-R and command-option-R revcoveries from boot up, nothing ever happens
-Tried safe boot, nothing ever happens
-Tried PRAM reset and SMR reset (the power one, I may have the name wrong)
-Tried booting up from the Recovery disk, no sucess
-Tried booting up from a USB recovery disk, which I made on my iMac
The last shot actually once got me to the disk utility. I was able to run to "reapair disk" to my main HD with no problems found.  I than was in the process of running "repair disk permissions" when it went black again.  I have not been able to get back to this point, however.
I am BROKE, out of warranty, and would really love any idea anyone may have for a clean wipe/install.
Thanks for your help!

Answer 1

So here's an update:
Still constantly shutting down, but some new interesting things:
1. If the run the Apple server hardware dianostics (through holding 'D'), it is the only thing I've tried where it doesn't randomly shut down.  I've had this open for 1+ hour, and no shut down.  This makes me think it's not hardware related, but I'm just guessing
2. I installed a fresh copy of ML on an external HD, trying the directions in the above article.  It did not show up in the options of bootable drives when I held down 'option' on boot up.
3. I then came across this: http://www.macworld.com/article/1167857/how_to_make_a_bootable_mountain_lion_ins tall_drive.html
Using this method, the external HD did show up as recovery disk, which I was able to boot up.  I got through the first several screens of a fresh ML install when it froze this time, right after the long progress bar.  This is the futherest I got through any method.   I have, sadly, not been able to get back to that point since the first try, though.
4. I have been able to get the globe from an internet recovery off of the internal partition recovery drive, but after the progress bar and the spinning globe, I just get the linen background, with the cursor stuck in the upper left hand corner, and no dialog box to top bar.
5. It seems like I can get further after I've given it a break.  With that in mind, I gave it several hours rest, then was able to log all the way in for about 15 secs.  I managed to take this bad photo just before it went black again (sorry I missed so much of the crash report):
Sorry for the bad photo, it's all I had time for.  The last time I saw one of these, the BSD process name was a file related to Magician, a monitoring program.  This time it looks to be related to Sophos.  This being different makes me then think that it isn't third party software causing the problem, but instead Apple's kernal.  Once again, this is just a guess.
Ideas?