after you have backed up run a check on your drive - Windows has them plus most manufacturers have a free utility that will check the drive for you - I have Western Digital's version which is Data Lifeguard and also their Diagnostics too. Check you drive name and work from there.
Also check your guarantee/warranty - I was suprised to have a 3 year term - when a 250Gb WD drive failed they replaced it with 500Gb!
Oh and if the drive does go badly wrong before you have backed up and you have another PC remove the dodgy drive, wrap it tightly in cling film and put it in the freezer for a few hours - this can work wonders and you can get more data from it before it fails again!
Get an external hard drive and start backing up all ur data, the hard drive is failing. if the hard drive does stop as ur copying ur files, then do as Rahere reccommends and put in freezer then try again a few hours later.
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If you have never cleaned the inside of your computer in the couple of years of owning it, then they could be a great deal of dirt/fluff in there, even in the cleanest of homes you still get the fans drawing in dirt/dust/fluff.
After you have unplugged the computer and grounded yourself by touching a water pipe for example, take the side of the PC off and brush ALL the fans with a small paintbrush, you may also find that there is fluff etc lying in the bottom of the case which will need to be brushed out.
The best thing IMO for cleaning fans is a can of compressed air, if you happen to have one of these, it provides a better/easy cleaning method than using the paintbrush.