ok i can tell you exactly what the problem is. RMA your sapphire 7850 and buy a different card. i had this exact same problem, sapphire were using cheap parts in their 78 series cards and it was causing too much power to go through a single capacitor. just google 7850 black screen you will see many many people with the same problem. it happened to me with my sapphire 7870 ghz edition so i rma'd it and got a gtx 670 instead had no crashing problems since. its not your psu and its not your ram (if your ram was faulty it wouldnt detect it or it wouldnt boot depending on the fault).