I presume the old harddrive is an IDE?
You could take it out and connect it to your new pc as an extra drive. Depending on what connections you have inside your new pc on motherboard, if there is no IDE connector you can buy a adaptor for a sata. Or you could buy a cable IDE to usb (you will need one with it's own power supply if you haven't got a spare molex 4 pin on new pc)
No need to fit the IDE harddrive inside new pc, you can just rest it on your desk (I put mine on top of a cork tablemat) Jumper pin on IDE drive should be set to Master.
These on Amazon will give you a few ideas for deciding best route with what you already have. IDE cable adaptors