Ok - I have some questions to ask you real quick:
1.) Have you ever opened your Xbox and tampered/unplugged and plugged back in your hard drive
2.) Have you ever replaced your old Xbox hard drive with a new one without formatting it
3.) Did this just happen after an update
If you answered no to all of the above, follow these instructions: Contact Microsoft Xbox Tech Support. You will need to have an untampered Xbox [as in the warranty sticker not removed. If you ever opened your xbox, you no longer have a warranty on it], and also an intact Serial Number located on the bottom of your console. There should be a black sticker on the bottom. On the top of that sticker, there should be something that says S/N. The string of numbers after that are what you need to give to Xbox Tech Support. Also, make sure this console was not used before you because if someone else registered the console already, you will not be able to fix it. Make sure you let tech support know everything that is going on, and they will help you as much as they can. If they can't get it fixed over the phone, with the warranty stuff checklist that I generously typed above all clear, then they will request you to send it in to get fixed.
If you answered yes to answers 1 and/or 2 and/or 3, please follow these instructions:
[WARNING: Make sure you have somewhat experience in windows batch and somewhat advanced computer knowledge. Just because you know how to play games on a pc, and know how to install a program does not mean you can do what this tutorial will tell you to do]
In order for me to keep this answer short, I am going to recommend a YouTube video that explains everything that you can do to recover your hard drive - I have used this on my friends Xbox Consoles, and I never had one issue with it when it came to the E101, E102, E103, E104, and E105 Errors. In this process, you will loose everything on the drive. Make sure that this option is your last resort [As in if you have no warranty sticker, do this. If you still have one. Don't]
Before I link the YouTube video, here is what we need to do:
1.) MAKE SURE THAT YOUR WARRANTY STICKER IS IN TACT. IF IT IS, DON'T DO THIS. IF IT IS CUT ALONG THE LINE OF THE PLASTIC OR IS NOT FULLY ON, THEN CONTINUE. OTHERWISE, FOLLOW MY OTHER RECOMMENDATION. I CANNOT STRESS THIS ENOUGH
2.) Using the Xbox one tear apart tutorial on IFixit, take off the front, and top of the console [Make sure you are very careful, and follow the tutorial completely] DO NOT TAKE ANYTHING OFF OF THE MOTHERBOARD. ALL WE NEED TO DO IS OPEN THE XBOX - (Link: Xbox One Teardown)
3.) Unscrew the chacey that hold the 3.5" sata hard drive. Make sure you take off the sata cable from the hard drive
4.) Make sure you have a PC that has both a sata power and cable available. Plug in your Xbox hard drive into that computer while it's off.
5.) Boot up your PC. In windows, go to control panel. Search for Disk Management. Look for your hard drive from your xbox. Right click on one of the partitions of the hard drive. [They should be named something like: User Content, System Update, System Update 2, ect.] Click the option that says delete volume. Do this for all partitions.
6.) Now, watch this YouTube video for what to do next. The person in the video explains it better that I can. (Link: https://www.youtube.com/watch?v=GaKVBo3k...)
7.) Now you should be set. Make sure you let me know if this worked or not.
Have a good day!