Searched for this error message and someone on the Microsoft page said that this could be related to faulty system partition.
Someone else said that Error f3-f100-0004 appeared because he has cancelled the 'erase data' process (turn off manually) on recovery mode.
The process was actually deleting the partition and format it.
Did you try to reinstall the OS using the recovery disk or the HDD recovery?
If not, try this…