Cannot login to store/iCloud and cannot restore iPad

I have an iPad mini 16Gb, running 8.3. Since yesterday, I cannot login into the store, nor iCloud from iPad. I used iforgot and have ensured my credentials are ok using the PC. Normal web access (safari) is fine.

In face of this, I decided to wipe the iPad and just re-install it. But I couldn't get it to work (nor upgrade to 8.4) because, it seems, it tries to phone apple and (again due to the login block) the iPad cannot do it.

I tried find my iphone to wipe remotely, and it says device is deactivated (despite it being connected and the feature switched on in the iPad).

So i tried to wipe or upgrade using iTunes. The iPad connects fine, it suggests the upgrade, but after it downloads and unpacks it - you got it - it says it's triying to back it up first, and iTunes gives up too.

So, it seems I cannot login/contact any of apple's resources from from within the iPad NOR can I force reinstallation from outside (iTunes). Any suggestions on what may be hapenning and how I can (at least) factory reset it? Many thanks!