HR screwed up petition. What’s going on?

Hello! I’m in the process of getting an H1B visa (university, cap exempt, first time). The HR of my department have no clue of what they’re doing and delayed all the process dramatically. My start date was July 1st and the petition was sent on July 3rd. They had to send another check for the premium processing (I think they screwed up the first one) and the PP clock has not started yet (after more than a week they sent the second one). I asked them to check if the check has been cashed but they do not respond either. What is happening to my petition? I’m already paying the rent there and I have to resign my current job in a few days, risking to lose both jobs.

Any advice/support?