The fact that you suspect you might have an old account probably indicates that you do indeed have another account. With that said, I don't think FortuneJack would outright just keep your money after detecting you have multiple accounts.

Maybe you should provide us screenshots of exactly what they said, so we can be better help gauge who is in the wrong here. I can't see any reason why they should be able to keep your money simply for multi-accounting, unless your other accounts somehow stole money from them or owe them money.

Imagine opening two bank accounts with the same branch, depositing $10,000 into each, then being told your second $10k is gone because you've got two accounts. Sounds ridiculous.