Ubuntu 16.04 freezes, Unity and 2D gnome, hard shutdown required

After a clean install of 16.04 after a HDD failure, system is randomly freezing on me, requiring hard shutdowns multiple times per day.

Clean install of 16.04 and boot onto 32GB SSD. Home and data partition on new HDD. New 16 GB ram added to existing 16GB ram in place of 4GB pair. Dell XPS desktop.
Holding down the shift key during startup does not produce a grub menu to do Memtest.

Del diagnostics indicate that all hardware is working, specifically no memory problems.

32 GB memory, and 12GB swap on a HDD partition. Freeze occurs with swap on and swap off.

System freezes either before (10% of the time ) login, or after login.

After login:
System freezes in Unity.
System freezes in Gnome flashback 2D.
Entire system freezes, Atl-PrtScn REISUB does not work, short power button press does not work, hard shutdown required.

Before login (only about 10% of the freezes):
REISUB works sometimes, other times not. Short power button press sometimes brings up shutdown dialog, but does not respond to mouse or keyboard input to finish dialog, and hard shutdown is required.

After login, system problem detected dialog opens about 50% of the time, with a unity settings daemon error.

Any suggestions for how to trouble shoot this issue? This is not only making me worried about creating issues for my new hardware, it's complicating my attempts to pull the last bit of data off the failing hard drive (and slighly corrupted back up as well).

Thanks!