Nice briefcase
It seems like the SSD is dead, but just to make sure...
Did you write down the error message from the Blue screen? if it flashes too quickly, try to see if you can get it up and running for a few minutes and then use this tool ( get a read on the blue screen, and from there just google. Alternativly you can connect the SSD to another computer and use the tool.
but as I said, It does seem like a broken SSD, so I would try connecting it to another computer and run an error scan from HD TUNE (http://www.hdtune.com/ - use the FREE version), and use heavyload (http://www.jam-software.com/heavyload/) to write temp files to it. You say the SSD disconnects after a few minutes, so try to see if heavyload and HD TUNE makes the BSOD appear faster - if they do it's a broken SSD controller.
I hope you find the faulty component, there is nothing worse than an unresolved error!
