Computer Bootind Windows 7 Blue Screen Appering?

I've been scouring the internet and can't come up with anything.Its an older computer, probably about three or four years old, running windows 7.The Symptoms: Repeated BOSD, Very Slow Operating, Won't allow for a Windows Back-Up to be made, has trouble booting into Windows.A while back before everything started, I had been using it and noticed that it had been running very slowly. It would operate fine for a while, before just seizing up almost completely. That went on for quite a long while, possible four or five months. Then things got worse.A few days ago, I noticed that it said that it had a hard-drive malfunction upon start-up, so it wouldn't let me boot the machine. So, I created a windows recovery disk off of another computer and tried that. That allowed access to the Windows Log-in screen and once beyond that, windows would operate as usual.But some of the times not even the start-up disk will get you in the front door it seems. They've tried to create a windows back-up file on an old external drive we had around, but it said there wasn't enough room. So after purchasing a brand new external hard-drive, they instead got the message "could not complete", again, sadly I wasn't there to see if there was more to it than that.So this begs the question, what exactly is wrong here - and more so, can it be fixed?I don't mind spending some time on it, I don't. I just need to know what to do really. I'm not sure if it is a virus that has gotten in so deeply or possibly malware that has corrupted windows itself. It could be bad memory, a HDD malfunction. Possibly Software or Hardware issues. I'm not really sure here at all. I've tried what I know and that apparently hasn't been enough.