Inspiron 5559 won't boot fully after update

I have an Insprion 5559 laptop that I bought in March 2016. I am not a fan of this computer in general because it is often quite slow. Last night, not for the first time, I was unable to save my work in Excel without it freezing up and the program crashing. In the past, I have fixed this by updating Office. I couldn't see how to do that last night (I always just find the update from a banner that appears at the top telling me there is an Office update, but there was no such banner), but I did have a windows update. So I started installing that and went to bed. I don't know what the update was, but I think it was a features update. I think I was most recently on Win 10 1703.

This morning, I went to use the computer and it was asleep/unresponsive. I held down the power button to kill it and then turned it back on. It showed me the Dell logo, then went black, then the next thing I knew, it was off again. I tried turning back on, and this time after the logo it went to an all gray screen with pixel-y gray lines across the entire screen. Eventually that went away and it went black again. I never got into Windows or even the login screen. 

I am seeing all these diagnostic tools to check hardware, but if I can't even boot to Windows, how do I run those? I guess it could be a screen issue, but I don't know why that would have just gone bad overnight. The battery has not shown any issues so far and I have still been able to get ~2 hours out of it. I don't think it is a power issue, because the screen did come on and I could hear the fan.

I'm afraid this thing is just shot. Which shouldn't be surprising, it was only a 15-month warranty period, so Dell obviously didn't think they had built a quality product. If I can't get it working again, I'll probably never buy another Dell again, because this computer has never been great.