your upgrade serial number is still good. if you failed to deactivate on your old computer(s), you may need an activation reset.
you don't need to install cs3 to install your cs6 upgrade. you will need both (c3 and cs6) serial numbers.
if you need the cs6 installation file(s) and if you follow all 7 steps (especially steps 1,2 and 3), you can download here: http://prodesigntools.com/adobe-cs6-direct-download-links.html
and activate with your serial number.
if you have a problem (error message, unavailable page or you are offered a current adobe version), you did NOT follow the directions.
the most common problem is failing to meticulously follow directions 1,2 and/or 3 which are needed to add an adobe.com cookie to your computer that allows you to download directly without using the akamai download manager.
again, follow the directions and you'll have no problem.