lightroom 2 invalid serial number

HI everyone,

I purchased lightroom 2 - via disk format in 2012. I have since misplaced the disk however I know the serial number. I have a new computer and cannot access my old one at all. I have downloaded lightroom again but when I type in my serial number it comes back saying invalid. I understand lightroom 2 is discontinued but is there a way to get it to work without having to pay again? I originally paid over $600 for the product, would be a massive waste if I cannot use a 'life time subscription/product'. I have tried chatting to adobe support but they have been less than helpful. Thank you