My (2012) iPad has stopped working. It's battery does not appear to be charging

My iPad is less than three years old. It has been working very well during that time. I have always kept its software up to date. A few days ago it's battery appeared to be having trouble charging. All I see mostly now (when connected to my laptop or a battery charger) is a completely blank screen with the occasional Apple logo appearing for a second or two, the occasional illustration of the USB connector for another second or two or the occasional battery indicator screen showing a thin red line at the bottom (indicating no battery life left). When linked to iTunes I am prompted to "update" or "Restore" but the device is not being recognised so I can't take either of these actions. I am completely stuck. Our family has used Apple products for several years and this is our first major problem - they are normally ultra reliable. Anyone got any advice about this?