What you can achieve depends on the drive and set up, being store bought I highly doubt they used raid (multiple drives as a single drive), so that means we are dealing with single drives, thats a major plus, now without knowing how badly the drive was corrupted we can't be sure what to expect, so I will start with plan A, and I have a small hope it will be all thats needed, but it will require you to open the sides on the new and the troubled system, are you going to be OK with that ?
Don't panic if you've never been inside a system before, so long as your comfortable following instruction we can walk you through it, so what I will do here is tell you what we need to do, and once you look inside with the instructions here and you feel confident to go ahead and try then great, if you still have doubts, or your worried about something in the way let us know and we can tell you what to do and expect, so just holla if you need more info than this, but needless to say take care not to damage the board or anything while inside there.
To start remove the mains lead, then remove the side of the troubled system, this will be 2 screws on the edge at the rear, some use thumb screws so you don't need a screwdriver, others you need a cross head (pozi) one, you will also need this for removing the hard drive from the troubled system.
With the screws removed the panel can be removed, some are stiff, others fall off almost, but "most" sides slide back away from the front for an inch or so, then they can be lifted off, next position yourself and the case in a convenient place to work, laying the case on it's side so it's flat is often a help for most of this procedure.
Now remove the 2 leads from the hard drive, there are 2 kinds of hard drive, ide and Sata, they are easily identifiable, basically the ide drive has a really big data plug (2" or so wide approx), Sata are much smaller, take note of each lead as it comes out, they are shaped so will only fit 1 way, so with that in mind by looking you will know what to expect, if it's ide note which way up the notch on the plug is so you know how to plug it in shortly.
The only thing left now is to physically remove the drive, there are anything from 2 to 4 screws, there "should be" 4, but it depends on who put it together, and TBH 2 screws are fine really given most never touch the system after it's placed where it's used, so undo the 2 screws on the cage holding the hard drive, see if the drive is loose by trying to slide it back toward the rear of the system, don't force it, if it doesn't move easily there is more screws on the other side.
To access those stand the system up if needed, and remove the other side panel in the same way as the 1st, but when you try to slide it you may need to use some force, in my experience they are pretty tight, one trick I use if it is that tight is get a flat head screwdriver, now insert it at ANY vantage point on the rear edge and twist it, the side should move easily when you get a good start then it will come off easily once loose, with that off remove the remaining screws and remove the drive sliding it toward the rear.
Thats the hard bit done lol, don't panic, it may seem like a nightmare but trying to explain it in writing is far harder than doing it, so don't worry as you read through this, just take it a step at a time and you will be fine.
With the drive in your hand, and only if it was an ide drive, you may need to change the jumper settings, in short there are 3 options, Ma\Sl\CS (Master\Slave\Cable Select), the drive will have a diagram or note about which pins are for what, I suggest setting it to CS, you may already find it is set to that, in which case leave it there, otherwise remove the jumper thats probably there, and replace it on the CS pins.
With the drive free you can move that case aside, now it time to remove the mains and side as you did with the other case, now you need to note if it is the same type of drive, or if it is different, it just means we connect it differently thats all if needed, and we will cover that if needed, so simply insert the drive into the cage, you will need to decide whether above or below the existing drive is better dependant on where the leads are (mainly ide drives here), and with the drive in place you can put 1 screw there to steady it if you like for sorting the leads, then remembering how they were plugged in on the other system plug them in again and we should be good to go.
There are a couple of points to note with the drives, first ide drives have master and slave settings, CS simply automatically selects the correct one dependant on which plug you use on the lead, so the master is ALWAYS on the end plug, and the slave on the middle plug, and dependant on how your lead is placed with the existing drive, and bearing in mind the notch on the plug has to be a specific way up.
You will find putting the drive on the wrong side of the existing one means you will have to twist this lead to get it in the right place which could damage it, hence the warning about seeing whether above or below is best.
Sata drives do not have that problem, BUT, the leads have edges\notches and they have to go in a specific way round, and it is not uncommon for these leads to break if they are forced, so take care with these connections.
I dare say there are numerous little bits I've overlooked, but hopefully you will be fine with this, needless to say any worries just holla and we will cover those as needed.
so with the trouble drive in the new system you can replace the side, only needs 1 screw to hold it really for this bit, you will probably find it easier to do this laid on it's side, when done stand it up and plug it ion again then fire it up.
All being well it will load up, but you may get a message saying new device installed restart to complete type message, just reboot the system, it's just acknowledged the new drive, it may not ask in which case great, now click on Start - My Computer and you should see the old hard drive showing, simply go into it and see if you can find your files and cut and paste them onto the new systems drive, which should be C as a rule, but I have seen exceptions.
The most likely place your files will be in is in the Documents and Settings - Your User Name - My Documents, obviously check out the other folders to check you haven't missed anything, this is ultimately what I hope you will be able to do, and assumes you can read the drive, if not then it gets harder, but a word of warning, should you get a message come up saying the drive needs to be formatted to use the drive say NO, this will wipe ALL data from the drive, and recovery is hit and miss.
Now to finish off with a few links to pic's to help explain some of what I have described above, then when you look at yours hopefully all this will drop into place, so see how you go, and feel free to holla with any questions\worries etc and we will help you through this.
Sata Hard Drive (gives a detailed look at Sata drives)
ide Drive (not perfect, but is hopefully enough to show what I mean)