Because you asked, “Does the screen need to be physically attached to the base in order for the touch to operate correctly?“ I just assume you haven’t tried operating it without it attached to the base. You should try that and see if it operates properly because as oldtutkey03 said it doesn’t have to be attached as long as it’s connected. I have seen generic parts customers bring in they ordered themselves act up because of exposed conductive traces being shorted by the metallic body of the iPad which can usually be fixed by covering those traces with kapton tape. In most cases you can tell the quality of the digitizer by looking at the color of the traces. The higher quality digitizer tends to have smaller gold or copper colored traces and the lower quality digitizers have larger silver colored traces. If it still does not work without being attached to the base than it may not be the traces, possible defective part or could be the ultra-rare software issue, which I only bring up because you said the original works fine, to me that points away from the touch IC. For that I backup if possible and just reformat the device but I definitely wouldn’t rule out a problem with the touch IC.