As most touchscreens have some sort of grid network arrangement to identify the "location" of the touch it may be that when you removed the touchscreen flex cable before removing the battery, and then when you reinserted the cable after replacing the battery, that you accidentally touched the cable end with your fingers leaving a film on a section of the cable end. This film may be resistive to electrical current and may make the touchscreen seem less responsive.
Obviously this is conjecture on my part but as you imply that it worked OK before the change but not so after this may be the reason.
What you need to do is open the tablet and remove the flex cable from the connector again and gently clean the connector end (the bit that slides into the connector on the systemboard or whichever end you removed) with Isopropyl Alcohol +90% and a QTip (ensure the QTip leaves no 'threads' as some seem to do) and then after it has dried, reinsert it into the connector and see if this restores it to normal operation. Take special care that you do not touch the flex cable ends again with your fingers when doing this or when reinserting them or alternatively use lint free gloves.
Here is a link which describes how touchscreens work.