Stake can trace the activity into your account and IP address within their platform. And I think, they're not going to impose anything that you haven't done.
But if they've seen you broke their rules, they're going to surely impose a ban to you if the offense is too big that would lead in banning. I also feel bad for the remaining amount that you can't withdraw but try to ask them nicely maybe there's some mercy they can show to you.
The advantage of having someone from stake that is active on the forum can be really helpful in deciding your case. But to be honest, a relatively large and well-known gambling site would not ban anyone from their website without any reason at all. Like what most have mentioned, will it be possible if you could provide a transcript of your conversation between you and their customer service? In this way, some might be able to help in resolving your issue for a speedy disposition of conflict.
Though I really doubt that you were banned for no reason, I am on the hunch that you most probably violated one of their terms and conditions that lead ultimately to your demise.