I've been running 14.04 on my work computer (Dell Latitude E6440) since last May with no issues. 4 or 5 weeks ago I upgraded to the 3.16 kernel and the newer X.org via the LTS Enablement Stack. Everything went smoothly until about a week ago when I started getting random screen freezes. A few times a day my desktop will freeze. When this happens, I can still move the mouse pointer but not between screens (I use the built-in display with 2 external ones). Ctrl+Alt+F keys don't do anything. Ctrl+Alt+Backspace (I've enabled that) seems to work sometimes but takes a really long time to restart the display server.
I've been looking at the X log, but nothing is popping out as particularly useful. How can I diagnose what's causing this? Any help is appreciated.