Empty gray screen on wake?

So I've been using this Mac mini (Late 2014, 2.6 GHz Core i5, 8 GB Memory, 1 TB HDD, OS X El Capitan 10.11.6) for almost a year now and I'm having a serious problem with waking up from sleep recently. If I let it sleep long enough, I get a gray screen on wake. No progress bars either, and it can go up to half an hour without doing anything. I disabled hibernation using pmset just in case, and the problem still happens. This has happened 3-4 times so far.

Incidentally, pressing certain buttons on the gray screen gives a system error sound. I'm not sure if that means it's a problem with OS X or not, but I'd wager it is, as I ran Apple Diagnostics and it showed that there are no are no hardware issues. I'm really confused now. Has anyone else ever experienced this?