Just thought that I would give an update on this!!
Yesterday, my wife had been using the "offending" iPad - after she had finished, I put it on charge.
Some while later I checked to see how far it had charged - nothing, zilch!!
Nothing I did would make it work.
My son came over this morning & connected it to a PC Laptop (using iTunes) &, without him doing anything to correct anything, it sprung into life - he was able to confirm that the Battery was holding a 100% charge, hence, it didn't appear to be a Battery issue.
He then disconnected it & it immediately died!
Nothing would retrieve it.
Eventually we made an Appointment at our nearest Apple Store (which is not too far away).
When we arrived, it was still dead, whilst we were waiting, it did startup, but then died again.
When the Apple Tech looked at it, he was obviously puzzled, but he connected it to an Apple Mac Laptop & the iPad came to life - therefore making it possible to run diagnostics - which revealed everything in good working order.
He then suggested that he would reload all of the Software (including iOS) to return it to Factory-Status (on the assumption that some software corruption maybe causing the problem.
On doing so, he did notice that certain stages took much more than the expected duration & seemed to lock the iPad for a while, before continuing.
By the time all this had finished (including re-setting it up) the iPad "seemed" to be working! But I could tell that he was hesitant that it had actually cured anything. Basically he advised that, if it happened again, he would replace it without further question.
We left the Store & went to have a bite - on arrival, a quick check showed the iPad working - by the time we had finished eating, it had failed again!
Straight back to the Store & it was replaced without any further query!!