Just to attempt to help you out here:

-If you had already redeemed the CD key on your old PC then you can re-download the game as many times as you want on any device (that can run it) so long as you can sign into and stay signed into that account. If you can't sign into the account you're SOL, Blizzard hasn't done physical since WC3 and that CD key is the product. Only reason you wouldn't be able to access the game at that point is if your account got banned, which is a typical practice with most digital storefronts (except Nintendo and Steam afaik).

-If what you're saying is you bought Diablo 3 having never redeemed the CD key since your purchase and when you did the service claimed it was already redeemed, then your issue is with the seller you bought the CD key from not Blizzard. The seller ripped you off and should try to contact them for a replacement since you have proof of purchase (unsure if there is any legal action that can be taken there).

Hope this was able to help :)