Just leaving my case for other struggling users.
I couldn't boot into USB installer and after install from DVD couldn't boot into Proxmox. After trying everything suggested on this forum I ended up doing these things:
disabling 'Fast Boot' in BIOS
changing 'Secure Boot' from 'MS Windows' to 'Other OS'
making sure all storage boot option had either 'UEFI' or 'Both UEFI and Legacy Boot' selected
This made everything bootable. So my old BIOS from 2013 wasn't the issue, it's always some BIOS settings.
I couldn't boot into USB installer and after install from DVD couldn't boot into Proxmox. After trying everything suggested on this forum I ended up doing these things:
disabling 'Fast Boot' in BIOS
changing 'Secure Boot' from 'MS Windows' to 'Other OS'
making sure all storage boot option had either 'UEFI' or 'Both UEFI and Legacy Boot' selected
This made everything bootable. So my old BIOS from 2013 wasn't the issue, it's always some BIOS settings.