Frequent freezes, white screen of death

I've been having frequent problems with my mid-2011 iMac 27". There's two basic issues. The first is that I'll come to use the Mac after several hours and I notice that the screen isn't completely black like it should be if it was asleep. There's a very faint bit of illumination to it. However the Mac will not respond to any keyboard or mouse activity to wake it up and I must forcibly power it off with the power button. After that it will seem to boot normally. The second issue is that I'll be working normally and all of a sudden the screen will fill with a blue and white stripe pattern for a few seconds and then go all white or it will just go all white immediately. When it does that it seems like it's not completely frozen because I hear some hard drive activity, but there is no way to 'wake' it back up. So again I have to forcibly power it off. This had been going on for several weeks and I was wondering if it was software related. I had been running Mountain lion on this, so last night I updated to Mavericks but after working for only an hour or so this morning the screen went white on me.

I've seen a lot of threads about people having the white screen on startup, but that's not what's happening here. Anyone have any ideas what might be causing these two issues?

Thanks.