It is a combination of two words: inability and cope. It means the inability to cope with a particular situation or event.
Can be used in any situation where you are struggling to cope (be it at work or play) but normally used in the context of being very tired, sick or hungover. I came up with it after a friend and I had a very large, late night out (basically we were dreadfully hungover and couldn't function normally the next day). "I don't know about you but after last night I have total inacopia today." Other examples where it could be used: after a heated argument with someone or having to sit through a dreadful meeting at work "It was bad... I had inacopia!"