Computer randomly shut down, and now won't reboot

So I have owned an HP laptop for a little over a year now, and it has never given me problems, until yesterday. I use the laptop for mostly searching the internet, and editing/storing photos. I went on my computer this morning, and it worked fine, but when I came home a few hours later to use it, it gave me problems. I tried to load a website and bam! it starts shutting down. I figured an update was going on, or something of that nature, but when trying to reboot, it goes to a blue screen with text on it, and then the computer suggests that I use the "startup repair" feature.

So, to make a long story short, I ran the startup repair, and it has been running for about 24 hours now, without a single sign of anything. It hasn't rebooted, or popped up any other screens.

My question is, what can I do to figure out how to resolve this issue? I don't care if any part in the computer happened to die, except my hard drive. I am a photographer, and literally had my first external HD die on me 3 days ago. I haven't purchased a new one since, and would hate to lose all the photos I have on this HD.

Sorry if this is vague, I will provide any other details needed upon request.