Black screen of death? something else?/saving my family pictures

Last night my 2011 iMac completely froze (very uncommon) during normal use. Upon restarting I heard the startup chime but the screen remained off. Attempted to restart several times over the last 24 hours with no luck and now I hear no chime despite the iMac being on, and the Mac is now shutting itself off after a short time. After some time it also stopped reading my wired keyboard (but not the wired mouse) for some reason. I've had my imac for 10 years and it has been very reliable for me despite slowing down a bit in the last couple years. It gets very hot at times but to the best of my recollection hasn't ever shut down due to overheating and this is the first time it has ever booted up with the screen not powering on. My 2 questions are

1. Does anyone know the cause of this? Am I experiencing the feared "black screen of death" and can I fix it? Even if the fix will only be long enough to get some of my family pictures off there.

2. If the computer is really past the point of fixing, is there a way for me to transplant my hard drive into another mac? I have had this computer for a very long time and I'm heartbroken by how many irreplaceable things I may be about to lose. I know at the end of the day it's my fault for not backing all of those things up. But any help that anyone can provide would be very appreciated.