Various pc problems I have

First problem came a long time ago, my graphics card went completely kaput, which is such a long story to tell I can't tell you here.

But now bew problems have arisen, first my PC was shutting down and restarting out of the blue, but a Windows memory dignostic managed to hold it down until a few hours ago when I'm typing this, I tried to attempt to do the memory dignostic again but it unfortunately stopped, (atleast I thought it did)

And NOW it won't turn on at all, well, it does but my monitor light never goes blue and my PC doesn't make a beep noise, which it always does when I turn it on, but the lights inside the PC glow though, and the fans were spinning.

I cleaned out some of the dust in the PC itself all the while unplugging all the usbs that were connected to the back of the PC, and it turned on then but I didn't manage to hit F8 in time to get to the repair my computer menu.

And now it's back to not turning on to an extent again, please tell me what's happening, I'm really at my wit's end now.

UPDATE: After a waiting a while and another Windows Memory Diagnostic, my pc is fine again, but it could happen again, hopefully this is something some people are familiar with.