iPad 3 not usable after updating to 9.3.6

You clearly state that your other devices are able to connect to internet resources, so recovery of your iPad to a working state remains possible.

Assuming that you either have access to a working PC (with iTunes installed) or a Mac (with Finder), you should still be able to reset and restore the iPad. Before doing so, you might wish to ensure that you have either an iCloud or iTunes backup.

When you’re ready to reset/restore your iPad, follow this procedure:

https://support.apple.com/en-gb/HT201252

As MichelPM has stated, you may have difficulties restoring some of your previously installed Apps. Otherwise, it should be possible to recover use of the device.

I hope you find this to be helpful.

If you attempt to erase and reformat this 8-year old iPad 3, if you do this before doing a thorough backup, you may never get all of your older apps for this iPad back!

These old iPad 2, 3, 4 and 1st gen iPad Mini models are nearing 8 and 9-years old, now.

As of the beginning of 2019, many, MANY third party app developers are all more quickly and completely dropping older app support for all old 7, 8 and 9-year iPads that are running 2-3 year old and earlier iOS versions ( iOS 10 and earlier ).

Third party app developers are removing all of their older, legacy versions of their apps from Apple's App Store servers, now.

Older versions of apps are going to be gone for good, now!

Getting older versions of apps for these old iPad models, initially from Apple’s iOS App Store is getting very difficult and very problematic and this issue is getting, painfully, much worse in 2020, now!

These old iPads are now reaching their complete end of life and support.

Old iPads that can no longer be upgraded/updated will have NO MORE APPS AVAILABLE for initial download, at all, soon, from the Apple iOS App Store, for such old iOS devices in the very near future.

Older versions of apps for older iPads will be completely gone, very soon!

To prevent this, if you own a Mac or PC, there is a special, older version of iTunes that can still save the actual app within iTunes ( something iTunes USED to do before Apple changed this feature/behaviour a few years, ago ) that still works with newer iOS devices, so, you can backup that old iPad 3, first, and save all the data AND older apps installed on that iPad before wiping.

You can restore these apps from this iTunes backup later.

Tap and read my own ASC user tip link to get the link for this older, special iTunes version ( iTunes ver. 12.6.5.3 ).

Head some of the stuff that is in this link as it is important for older iPads, as well.

Downloading Older iOS 9.3.5 Versions of A… - Apple Community

Best of Luck to You!