it's possible to move a hard drive from one computer to another
It;s also possible to buy an external enclosure and put the drive inside it and then connect it to another computer as a 2nd hard drive
While these can be straightforward to do, there can also be some issues if you;ve never done it before.
I think you are best to 1st see if you can boot from CD (i.e. the computer starts up reading the Operating System files and programs from a CD).
Means you need a bootable CD. Again, there are many options issues here but if this is all new to you i think best solution is go to your computer store and get Acronis True Image Home v10. Includes a bootable recovery CD and ability to read and transfer files from the old computer hard drive to another media. And when you're all done you have backup software to use regularly!