Chosen Solution

Some of the keys on my wireless apple keyboard are not working. I have tested it on a different computer and the problem persists so its not a software problem. The keys not working are space bar, backspace, caps lock, up arrow and tab

Sounds like you’ve worn out your keys. If you had a group of keys along a common group like Caps Lock, A, S, D & F then I could have seen one of the traces to the interface chip had failed. Here you have a scattering of keys. These keyboards are not really designed to be fixable (disposable) by Apple. It would be just easier and cheaper to replace it with a new one.