Bonjour Bernadette !

That's a very interesting question, and one that many students ask themselves: what is the difference in usage between l'Imparfait et Le Passé Composé.

In general, Le Passé Composé will be used for cases where the Simple Past is used in English (e.g. I ate, I did,...), to talk about actions that are considered as a whole, and finished in the past.

As for L'Imparfait, it's a bit more complicated: it is equivalent to the Continuous Past (e.g. I was eating, I was doing,...) when describing actions that last in the past, considered in their process. But it is also the tense to describe habits in the past (e.g. I used to...).

As for j'étais vs j'ai été, look at these examples: 

1. L'année dernière, j'ai été vraiment malade.             
versus                
2. L'année dernière, j'étais vraiment malade.

There is an extra difficulty which is the verb 'être', because the nuances I've explained are not as easy to sense with this ''state-of-being'' verb. Both cases would be translated in English by ''Last year, I was really sick.''

In the first case, you're talking about the fact of having been sick as a punctual event that happened at a definite point in the past.
In the second case, you're evoking that sickness as something that lasted in the past, in its temporality as a process (e.g. it would be a bit like saying ''I was being sick'').

I hope my explanation is clear enough, it is a very interesting grammar point, as these tenses' usage differs from their English equivalents.

Thank you for this challenging question, which I'm sure will help many other students!