From what I know, if you purchased a stand alone product, you should still have download link for that product from your Stardock Account https://store.stardock.com/myaccount/products . But, if you was on ObjectDesktop package, than you do not have it under your account. Unless you renew your subscription, which should now come with Tiles 2.0.
Yes, serial bought under tiles V1 not compatible for V2 and so should be V2 keys not working for V3.
Stardock Community Assistant.