Invalid Password El Capitan with Filevault encryption
I found that the problem was faulty ram after doing hardware diagnostic tests.  In order to do this you might need to boot from the Apple "ASD" images.  To find the correct one for your machine this website has a list of which ASD relates to each Mac product. http://www.dannydullin.com/apple-service-diagnostic-asd-reference-list/

After you know the "ASD 3S***" number you can then search Google to download the image files and write them to bootable storage as explained in the documentation stored inside the images.

ASD 3S108
iMac (Early 2006 17-inch)
iMac (Early 2006 20-inch)
MacBook Pro (17-inch)
Mac mini (Early 2006)
MacBook (13-inch)
iMac (Mid 2006 17-inch)
iMac (17-inch Late 2006)
iMac (17-inch Late 2006 CD)
iMac (20-inch Late 2006)
iMac (24-inch)

ASD 3S116
MacBook (13-inch Mid 2007)
MacBook Pro (15-inch Core 2 Duo)
MacBook Pro (17-inch Core 2 Duo)
MacBook (Late 2006)
MacBook Pro (15-inch 2.4/2.2GHz)
MacBook Pro (17-inch 2.4GHz)
iMac (24-inch Mid 2007)
iMac (20-inch Mid 2007)
Mac mini (Mid 2007)

ASD 3S123
iMac (20-inch Early 2008)
iMac (24-inch Early 2008)
MacBook (13-inch Early 2008)
MacBook Pro (15-inch Early 2008)
MacBook Pro (17-inch Early 2008)
Mac Pro (Early 2008)
MacBook (13-inch Late 2007)

ASD 3S132
MacBook Air (Late 2008)
MacBook (13-inch, Aluminum, Late 2008)
MacBook Pro (15-inch, Late 2008)
MacBook (13-inch, Early 2009)
MacBook Pro (17-inch, Early 2009)
iMac (20-inch, Early 2009)
iMac (24-inch, Early 2009)
Mac Mini (Early 2009)
Mac Pro (Early 2009)
iMac (20-inch, Mid 2009)
MacBook Air (Mid 2009)
MacBook (13-inch, Mid 2009)
MacBook Pro (13-inch, Mid 2009)
MacBook Pro (17-inch, Mid 2009)
MacBook Pro (15-inch, Mid 2009)
MacBook Pro (15-inch, 2.5.3GHz, Mid 2009)

ASD 3S138
MacBook (13-inch, Mid 2010)
MacBook Pro (13-inch, Mid 2010)
MacBook Pro (17-inch, Mid 2010)
MacBook Pro (15-inch, Mid 2010)
MacBook (13-inch, Late 2009)
iMac (21.5-inch, Late 2009)
iMac (27-inch, Quad Core, Late 2009)
Mac mini (Late 2009)

ASD 3S139
Mac mini (Mid 2010)

ASD 3S140
iMac (21.5-inch, Mid 2010)
iMac (27-inch, Mid 2010)

ASD 3S142
MacBook Air (13-inch, Late 2010)
MacBook Air (11-inch, Late 2010)

ASD 3S143
Mac Pro (Mid 2010)

ASD 3S144
MacBook Pro (13-inch, Early 2011)
MacBook Pro (15-inch, Early 2011)
MacBook Pro (17-inch, Early 2011)

ASD 3S145
iMac (27-inch, Mid 2011)
iMac (21.5-inch, Mid 2011)

ASD 3S146
MacBook Air (13-inch, Mid 2011)
MacBook Air (11-inch, Mid 2011)
Mac mini (Mid 2011)

ASD 3S147
iMac (21.5-inch, Late 2011)

ASD 3S148
MacBook Pro (13-inch, Late 2011)
MacBook Pro (15-inch, Late 2011)
MacBook Pro (17-inch, Late 2011)

ASD 3S150
MacBook Pro (13-inch, Mid 2012)
MacBook Pro (15-inch, Mid 2012)
MacBook Pro (Retina, Mid 2012)
MacBook Air (11-inch, Mid 2012)
MacBook Air (13-inch, Mid 2012)

ASD 3S152
iMac (27-inch, Late 2012)
iMac (21.5-inch, Late 2012)
Mac mini (Late 2012)
Mac mini Server (Late 2012)
MacBook Pro (Retina, 13-inch, Late 2012)

ASD 3S155
MacBook Pro (Retina, 15-inch, Early 2013)
MacBook Pro (Retina, 13-inch, Mid 2012)
MacBook Pro (Retina, 13-inch, Early 2013)
iMac (21.5-inch, Early 2013)
MacBook Pro (13-inch, Mid 2012)
MacBook Pro (15-inch, Mid 2012)
MacBook Pro (Retina, Mid 2012)
MacBook Air (11-inch, Mid 2012)
MacBook Air (13-inch, Mid 2012)

ASD 3S156
MacBook Air (11-inch, Mid 2013)
MacBook Air (13-inch, Mid 2013)

ASD 3S159
Mac Pro (Late 2013)

ASD 3S162
MacBook Pro (Retina, 13-inch, Late 2013)
MacBook Pro (Retina, 15-inch, Late 2013)
MacBook Pro (Retina, 13-inch, Mid 2014)
MacBook Pro (Retina, 15-inch, Mid 2014)