I have a 2011 MacBookPro running OS X Yosemite. I was browsing online when suddenly my entire screen went grey (no cursor, completely unresponsive). I restarted the laptop & got the usual "Update Needed" user (I have FileVault on). As soon as it reaches halfway thru the progress bar, it reboots on its own! I tried resetting the SMC, as well as holding down Cmd + R to access recovery. In the latter case, the Apple logo appears with a progress bar underneath. As soon as it reaches halfway thru, the screen turns grey & it just sits there. The same thing happens when I try to boot into safe mode.
Tried many times unsuccessfully. I have a feeling this has to do with FileVault.