And I can now enter the PunkBuster server.
But can't enter the bf4db server

Claim your account first.

There's a CLAIM button on your profile page. Follow the instruction to claim your account.

First of all, thanks for bringing that BF3 PB Violation #71512 up. It can be used as an minor additional evidence.

You got banned for PunkBuster Violation #89396, which is for BF4 and is directly streamed to us.

According to our BAN POLICY, Punkbuster Violations that are streamed to BF4DB are grounds for an immediate ban. 

PBBans is not Evenbalance, so that's why there's no #89396 Violation to be found on PBBans.

Appeal your Violation by creating a support ticket on http://www.evenbalance.com/support.php.

If EB admitted that your violation is triggered by mistake, include your PB support ticket link in PM or another appeal. 

For now,

APPEAL DENIED