The Sony VAIO is the computer you're talking about, right? Frankly, I think this is a goofy idea. Nevertheless, if you really want to do this, I believe you need to confirm that the Sony does not have proprietary components (motherboard, power supply, etc.) that will not fit in a standard ATX case. I don't know the answer to that.
You might post the exact model of your Sony. Perhaps someone can help with that additional info.