Root how to access memory in a tablet (Tablet freezes on the welcome screen)

Not really the correct place to ask this question, as this forum is specifically for the HTC Rezound phone, and even more specifically for questions regarding root-related matters, but I will give you little help...

Have you tried ADB? Will the tablet connect and can you use ADB when it is booted up as far as it will go, or is that turned off as well (the default in most devices unless it was manually turned on), I am assuming no...

If you have a "noname" tablet, stock, unrooted, with no custom recovery, no ADB access, and no way to do these things, you are most likely out of luck. Your recovery options would cost 10x what the tablet costs, most likely destroy the tablet, and would just be a 50/50 chance anyway by sending it in to a data recovery service and see if they can read the storage chip directly.

Your best bet at this point would be to try to figure out the real manufacturer and model name, hope it has some support in the developer community with a custom recovery like TWRP -AND- some way to flash it from the bootloader -AND- that it can give you access to the storage or OTG access (assuming you have an OTG cable, with power if needed)... And this is a long shot, because many TWRP builds for oddball devices don't have these features built in, but it is the best longshot I can give you.

Honestly, there is a reason people have devices with external storage, like microSD, and set pictures and other important data to be saved there, or/and use clould based storage on an automated basis, like Dropbox, Google Drive/Photos, or whatever, because devices fail... they just do, some go an extremely long time and some do not, but all will fail eventually. If you took my beloved Nexus 4 of 2 years and dropped it in the river today with no warning, I would be out nothing, except the device itself and a few days or weeks worth of text messages at most, because everything is synced to the cloud on an automated basis, thousands of pictures, videos, all contacts, emails, downloads, SMS/MMS backups, etc... its all there and could be restored or accessed at any time.

I am sorry you are in the position you are in, and I wish I could help more, but the best I can do is say try the handful of things I mentioned, and if they are not possible, use this as a learning experience so it doesn't happen to you again.