rom – Need to flash Galaxy Tab PRO 10.1 to recover data

I hope you can help with this problem:
Samsung Galaxy Tab PRO 10.1 SM-T520 Kitkat 4.4.2

This is my wifes tablet and recently stopped booting into the second Samsung logo.
This is what happens after the purple swirly (sorry for the technical term).

I went through some simple things to try to fix it, including restarts.
I also disconnected the battery for a while while pressing the power switch.
I hoped that this could clear up the problem, but it was not like that.

I tried to connect to my PC wifes where it was not recognized (it used to work there).
I also tried my system, did not have any SW installed, I tried the latest version of Kies.
I also tried an older version of Kies and also Samsung Smartswitch. Later I also tried Odin.
Nothing recognized that the tablet was plugged in. I tried several cables in vain.
If I search in the hardware manager on both PCs, no tablet will appear.

It looks as if the USB tablet is dead or the SW is not working enough to enable it.

I did some research and went into recovery mode, this is what comes up.

Android system recover <3e>

Android dead with "no command" below

In my research I discovered that you can update an image of the SD card.
So I found two roms in the United States (XAR region) for Kitkat 4.4.2, I've tried both.
I used "apply external storage update" in the recovery menu and selected the ROM.
It seems that they begin to load or be extracted in the tablet and then the following appears;

E: the footer is wrong
E: error in the verification of the signature

The previous message happens twice. The only reason I have not resorted to the factory settings is that my wife did not back up the tablet in the last 6 months and the previous backup has empty directories. While nothing is critical on the tablet, she has saved many quilting / clothing designs for free.

So, whatever I do, I'm trying to preserve the data, hence my efforts with the ROMS.

I can not change the configuration of the tablet, I can not get the USB to work and I keep getting errors with the ROMS. I have seen that it suggests that slow downloads can damage the zip files I am downloading. I do not want to pay for the download. Is there any place to get free ROMS at a decent download speed to rule this out?

Anyone has any ideas for anything else they can try.

Thank you