Given the lack of sleep, probably a little of both, maybe more of the second. ;)
How do you differentiate between the words old and sleep? They are both translated as ישן in Hebrew.
The vowels are different. So if you had to specify, you'd write it with vowels.
Actually it should be accepted as in Hebrew they use this construction for both "I don't" and "I can't". For example:
אני לא שומע אותך
I can't hear you.
Oh ok. I was confused because in some cases I've seen cannot, don't and am not translated the same.
In idiomatic English, at least in Australia, 'I don't sleep' is often interchangeable with 'I can't sleep' I think it should be accepted. (This is similar in a way to how Americans will tend to say 'I don't see the car' while Aussies are more likely to say 'I can't see the car' - they mean much the same thing.)