JulieCorky - I am enjoying a similar problem with my 10.1.
Were you able to do a Factory Reset or a Hard Reset? Pressing the power button AND the Volume UP button at the same time, releasing the power button when the unit powers back on and presents the Samsung Galaxy Note 10.1 screen is how I understand you should be able to get to a reset screen. The disclaimer I have read, you will lose what you have on the tablet. When it logs back into your account you 'should" recover. Recover or not, all is lost if it will not power on. Give it a go, I hope it works for you, it is not working for me.
NOTE: Doing this will clear 'all' the data on your phone, so it is suggested you not choose this option unless you have to, or aren't worried about losing anything on the phone.
Be sure you back up any data you want to keep, to a computer or cloud account, before doing the reset.
To "Hard Reset" the phone...
1. Make sure that the phone is actually powered off.
2. Press the "Power" and the "Volume Up" buttons, together, until you see the start-up logo on the screen.
3. Once you can see the logo, release the buttons and allow the device to enter the "System Recovery Mode".
4. Next use "Volume Down" button to get to the "wipe data/factory reset" option When in recovery mode the "Volume Up" and "Volume Down" buttons are how to can navigate and highlight what option you need.
5. Once you have selected the "wipe data/factory reset", press the "Power" button to select that option.
6. On the following screen, repeatedly press the "Volume Down" button until the "Yes - delete all user data" option is what is selected.
7. Then press the "Power" button to hard reset the phone.