IPAD Air No longer lists or supports Bluetooth Keyboard(s)

I was on holiday and my keyboard failed. It was run on batteries - a Logitech. I went to purchase new batteries but it still did not work; the assistant said, look at the Bluetooth - I did - there, as usual my two keypads were listed under bluetooth but clearly the Logitech was not pairing. I return from holiday, convinced the problem is with my Logitech, so I connect to a electric Belkin keyboard. The keyboard does recognise the ipad as it lights up when connected. However, this does not work the other way around; Bluetooth no longer lists any keyboard and continually spins and spins. For one moment it listed some Galaxy device that I have never used, owned or heard of, then and now, it continues to spin. I have read every single page on the web and have tried switching everything on/off/ rebooting etc etc. Nothing helps. Apple support totally useless. Is this the end of using an IPad? Because without an external keyboard it's just a piece of junk to me.