If the other PC is now not working (because he has removed the parts) then the hard disk will need to come out and be used elsewhere.
The two choices are to install it inside your existing PC case as a second hard drive, or to buy an external hard disk case and put the hard drive in it.
Then you can use a product like Acronis True Image to clone your current harddrive to this new hard drive.
You need to find out how big the hard drive is in the "new" tower to see if it is worth it and has room for the clone (if it is an old hard disk it may be very small compared to newer hard drives)..
You also need to find out if the "new" hard drive has a IDE connection or a SATA conection (to know how to "fit" it).
If neither of you have done this sort of thing before there has to be a bit of "trial and error", but then that is the best way to learn.