Black Screen, now recovery discs won't work

Last week, I posted this:

Go easy on me please, I'm not all that tech savvy.
I was using my computer with no problems for a little while yesterday and then walked away for a while. When I came back I had no internet connection and my computer couldn't even see any other networks, which is weird because even if my modem isn't working, it will always see my neighbors' connections. Anyway, so then I left for a little while and when I came back to it, it had a black screen with a bunch of random letters filling up the screen. I don't know how long the screen was like that before I noticed it. So I immediately did a hard restart. When it restarted, it went to my normal desktop and after a couple of seconds and the screen looked like it just melted. It turned black with a bunch of blue dots all over the screen and the alert sound was playing constantly. So then I went into safe mode to try and restore to a previous version and that didn't help at all. And after a while of messing with it I can't even get it to go into safe mode anymore. So I did an entire system restore (or tried to anyway), and it got most of the way through before it just stopped running. And that's where I am at this point.
I'm looking for any advice at all of what I should do. Wondering if this is a virus, and if so does it sound like I can just replace the hard drive and be done with it or could it be something worse? At this point, I'm not too worried about losing any data as I backed up my files not too long ago, but this is a relatively expensive computer with a lot of upgrades so I'd like to keep it. Thanks!

The point I'm at now is that I've installed a new hard drive and am still having a similar problem. The system restore gets most of the way through before it stalls, blue dots covering the screen. I posted this on another forum and people basically said that I am not being patient enough to let it finish installing. I'm not a computer genius, but I do know when something isn't right, and trust me when I say it wasn't right.
So anyway, I tried with the entire system restore when that didn't work, I then tried using a Vista disc that I had lying around to see if that worked, and it did to a point. I am now able to boot from the disc and use my computer that way but it's only temporary and and will not fully install. In other words, if the computer shuts down, it has to go through the installation process again before starting upand getting to a point where I can use it, but it loses everything like saved passwords and internet history. Or if I remove the disc, the computer will not work at all. So basically it's not good for anything but internet right now. I've tried replacing the hard drive and that didn't work. Any ideas what this could be?