You may be able to make a claim through your payment provider - bank/credit card.
As you have discovered, once you close a case, you can't re-open it.
Never close a case until you are 100% satisfied that your issue has been resolved.
"There are two ways to be fooled. One is to believe what isn't true; the other is to refuse to believe what is true.”
Søren Kierkegaard, Danish philosopher (1813 - 1855)