CD-RW for laptop

Okay; I'll be leaving home soon, and leaving my old computer behind (it's not much use anymore, but my parents will be able to use it for what they need). I would, however, like to keep the CDRW I put in there for my laptop.
My question is: is there any way I can convert or otherwise make operable my internal CDRW for a pc, so I can use it with my laptop? If I can get away with using this instead of just buying an external CDRW, I will.

I should mention that my laptop is a Toshiba 1800 series Satellite; it's running Windows ME, and it has a DVD Drive inside already. Thanks for any help.