She was typing on a computer keyboard.

That is grammatically fine, but I suspect that it contains redundancy in the context. That is the only kind of keyboard we use nowadays.

In what context can I use it as a standalone sentence?

I remember that I was warned by many non-native English teachers to use the past continuous rather rarely - mainly in situations that refer to:
a) an interrupted action in the past
She was typing on a computer keyboard when her telephone rang.
b) a specific time as an interruption
Yesterday at this time, s

ReegisIn what context can I use it as a standalone sentence?

Your question gives you the answer. The sentence needs context, such as someone asking "What was she doing when you saw her". The sentence cannot stand alone.

So my information is correct Thanks for your confirmation, fivejedjon.

I have just come across one more sentence with the past continuous that seems non-standard to me without context:

The children who were playing near the pipe are all sick now.

fivejedjon, could you please say whether it is correct and in what context you would use it?

ReegisThe children who were playing near the pipe are all sick now.

It is fine. They were playing in the past and they are sick at present.

Hmmm, so is there any difference between

The children who were playing near the pipe are all sick now.
and

The children who played near the pipe are all sick now.
?

Reegisso is there any difference betweenThe children who were playing near the pipe are all sick now.andThe children who played near the pipe are all sick now.

In meaning? No.

This is interesting... So can I use both sentences interchangeably?

Different ways of referring to a situation are rarely completely interchangeable at all times. However, for this situation, either would normally be possible. More context might make one more likely than the other.