Drop CMOS settings (remove battery for a minute), then connect old PSU. If system booting, enter the BIOS Setup and change option named 'Flash Update Sleep Delay', this option is for greater PSU compatibility. After this switch to new PSU & try to boot again (be sure to wait at least 20-30 seconds in first boot). If nothing helps, contact Intel support for RMA.
You sir are my personal hero of the day. Thank you very, very much.