There aren't many elegant solutions to this problem.
Here are a few videos to watch for help:
As XFiX said in the 2nd video, checking the system log helps. Plug the hard drive from the Xbox into a PC and check the system log. This starts at 6:40 in the video.
Here is a short checklist of things to check when E100 Error occurs:
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DVD drive (if there is one) should be attached to the Xbox and has not been tampered with/changed
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Make sure the HDD/SSD is not corrupt
From XFiX's video (DRIVE REFERS TO OPTICAL DRIVE):
The drive itself has failed and is not responding due to a bad circuit board component
Fixable? Maybe, as long as it's not the ARM chip containing the drive key
The drive firmware is corrupt
Fixable? Maybe, only if the OSU1 update is able to re-flash it (Original Xbox One may require OSU2 and/or OSU3)
The drive cables are damaged or not connected
Fixable? Yes, replace or attach the cables
The entire drive or just the circuit board was replaced with another that does not match the current system's motherboard
Fixable? Maybe, only if you can get the matching original drive or circuit board re-installed