Thank you for contacting the Intel Communities.
I would like to recommend you to check the power management settings in your BIOS that you may have in your system related to hibernation or S3/S4/S5 states.
Also, if when you hit the power button the CPU fan spins and the chassis fans also spin, my recommendation would be to check the boot order at BIOS level. If USB is selected as first option and you are connecting a HDD, it may be trying to boot from that drive which may not allow the system to boot properly.
Additionally, you could test if this problem follows the USB port or the device, meaning that you can try to replicate the issue using different USB 3.0 devices and different USB ports with current devices.
Check the voltages output from PSU (tools like HWMonitor and SpeedFan), especially +5V one. Over- or undervoltage can lead to USB malfunction.