System Won't Find Hard Drive/16.04 whole hard drive encrpted

[richardr369]

I'm still a newbie at this so I appreciate everybody's patience with me. I have run Ubuntu for years with no issues. Then one day my 16.04 froze and I had no option but to hard power down. I haven't been able to connect to my hard drive since. I burned to DVD, Boot Repair and attempted a basic repair. Their forum stated it was closed so I didn't post any cries of help over there.
The information that I was able to produce is located at:
http://paste2.org/EFMVZ32P
http://paste.ubuntu.com/24404611/

Does anybody have to patience to assist me?

[oldfred]

You are not even showing any drive(s) at all.

Does BIOS show you have drive.
If BIOS does not report drive to operating system, then operating system cannot find a drive.

If BIOS does show it, what does Disks show.
In upper right corner is Smart Status in Disks. It can run lots of tests, but all I know is good or bad.

Should never hard shutdown unless you have no other choice.
Best to remember the elephants first.

Never force shutdown your system. Use Alt+SysRq R-E-I-S-U-B instead. (For newer laptops they don't bother adding the SysRq print to the key, but it's the same as the PrtScr key)
Holding down Ctrl+Alt and SysRq (which is the Print Screen key) while slowly typing REISUB
R-E-I-S-U-B to force shutdown
A good way to remember it is, and S can be before E, but others should be in order
Raising Skinny Elephants Is Utterly Boring ...or
Reboot System Even If Ultimately Broken ...LOL.
https://en.wikipedia.org/wiki/Magic_SysRq_key
http://kember.net/articles/reisub-the-gentle-linux-restart/