Warning! Before you do anything else on the mini, be sure to understand that the battery connector must always be disconnected before you pull any other connector or the mini will lose its backlight fuse.--end of warning.
Since I'm sure you've triple-checked the socket connector, I'll tell you what I would be thinking.
1.) iPad mini fpc socket connectors are notorious for getting their pins knocked out from plugging/unplugging. Take a look at the socket under magnification---do you see a little gold tooth for each pin of the connector, or are there one or more missing ones? If so, that's it.
2.) If not #1, then I'd be thinking it's the digitizer ic assembly--either third party crap or got too much heat during desoldering if original.
3.) think bad soldering on digitizer flex, or kinked/bent flex
#2 and #3 are solved with a new digitizer assembly.
#4--rarely this would be damage somewhere else in the touchscreen circuit on the motherboard.
If you need help with an iPad mini fpc connector repair, give me a shout via my profile. If you try to DIY that one you could get into permanent damage very easily.