iPad mini won't boot or connect to computer

I have an iPad mini which won't boot. I thought it might be dead, so tried charging it, but even plugged in to the charging cable after charging overnight it will turn on to the boot screen and then abruptly quit. Tried hard reset, and connecting to computer, but I get the same thing. Very rarely when I try turning it on, I get past the boot screen to the password entry, but then it immediately shuts down again. The battery is a little suspect, since it is an older device, but I don't think it could be causing this problem as it persists even when plugged in to a cable that I know works. When plugged in the device also makes the charging 'ding' sound. This is puzzling me, any advice is appreciated. Thanks.