I had the same problem - and it's a super hassle to take the back on and off. So - here's what worked:
1) You do the battery replacement, and be super sure that the wide ribbon cables are gently, but fully seated before the clips are flipped down. Likewise the power (middle) cable is fully seated, with the clips on either side of the plug end fully seated. NOTE - when taking the back off, do the edge with the switches in it last. It's easy to snap the edge where the holes are for the buttons. I broke the volume switch hole, and had to super glue it very carefully.
2) Without putting the back on again, locate the little pressure switches on the edge that correspond to the back cover switches (the ones you'd normally use). There's one for the power, and two of them for the volume. The look like teeny bumps. Using a thumbnail, gently depress the power one, which should turn the tab on - but the screen remains unresponsive. Turn it off again (or wait a moment, it'll switch off).
3) Depress both the power and the volume up (I believe it's the one closest to the power, but it could be the other one - try them sequentially, not all at the same time) for 10 seconds, using a finger nail for each of the 2 buttons. It's awkward, but easier than putting the back on and off.
The tab then restarts, going to the all black screen, then the Tab S then SAMSUNG, etc. When that completes, the touch screen functions should be fully restored. If not, it's probably a ribbon connection.
Good luck!