I really could not find the problem. No one seems to have it. First, I replaced all cables with brand new. No success.
Then I started from scratch, even used voltage dividers instead of IC, but the result was exactly the same. Already suspecting faulty mp3 module, because I already checked SD module (have few of them) and they had no problems.
Right now I'm moving everything to universal pcb, without much cables and with connectors, so when my replacement mp3 module comes, I will check it.
Already thinking of doing one from scratch with VS1003/VS1053 IC by myself ... might be better 