IANAL but I'm afraid thats not legal,

1, your license was 'bound' to your old pc when you install the pro, you can't 'transfer' it to another pc, AFAIK,

2, even if you have not really installed the pro, you just have a upgrade media with upgrade license but never used, even then, installing the upgrade version on a fresh new pc, without a home version license bound to it, is still illegel, AFAIK.