Similar issue with a Macbook Pro but I have had Yosemite running successfully for awhile now and not sure what caused this without digging into system/debug logs...
After login, the install progress bar never made it past 20% and hung...forever
Tried all the standard keyboard start up techniques, please visit (OS X Yosemite: Ways to start up your Mac) Be sure to visit the links at the bottom too:
CMD + OPT + R + P (many, many, times...no luck)
CMD + T
CMD + SHIFT + V
CMD + R
CTRL + SPACE + RETURN (did not work either)
Tried all these techniques with all the prescribed steps associated to each start-up = no fix
Tried the "unsigned" extensions steps previously recommended:
<terminal>$system_profiler SPExtensionsDataType
keyboard shortcut: then CMD + F <search for Not signed> extensions
#note did not finding anything not signed by Apple
Google found this gem as I was pretty sure this had something to do with FileVault
https://derflounder.wordpress.com/2011/11/23/using-the-command-line-to-unlock-or -decrypt-your-filevault-2-encrypted-boot-drive/
<terminal>$diskutil corestorage list
or
<terminal>$diskutil cs list
~note I could see the encrypted volume...duggggghhh! My cat must have enabled it
Brain LED started to flicker...just barely (my problem was definitely related to filevault)
I pivoted back to my old friend: CMD + R
Went into disk utility
Selected main HDD
From disk utility file menu, choose UNLOCK
From same menu, choose DECRYPT
***NOTE, DO NOT UNPLUG YOUR MAG or POWER CABLE AS THIS WILL STOP DECRYPTION***
After decryption completed (for the record, since I could not get into the O/S, I had to keep booting into recovery tools, then opening up TERMINAL (in the File Menu) and checking by issuing this command <terminal>$diskutil cs list (just read the derflounder link above...it explains everything)
Reebooted...
No luck
Then, I remember I had a USB flash drive (e.g., 128GB stick) that had the Yosemite installer on it, turned off the Macbook Pro, inserted the stick, OPTION key down, power on, selected Yosemite Installer...
Long story short I was down for a day but the last step finally repaired my installation and I am now able to reboot normally and logon. going to do some backups, etc before I enable FileVault again
Good luck