Do you still have the old Mac?
Then launch Aperture 3 there: You can see your Aperture 3 serial number in the "About" panel:
From Aperture's main menu bar: Aperture > About Aperture.
On your new Mac enter both serial numbers: first the Aperture 3 upgrade serial, then the Aperture 2 serial number.
If you cannot retrieve the Aperture 3 serial number from your old mac, contact Apple, see: