This is generally expressed with "do not" in Hungarian, if you say it with "cannot" (Nem tudom megtalálni az orvost). it means something along the lines of "I'm incapable of finding the doctor"
Do you mean that my own defects prevent me from finding the doctor (nem tudom megtalálni), whereas 'nem találom' means other circumstances (outside my control) prevent me? But still, there's no distinction between 'I didn't find the doctor [not that I was looking for him in particular]' and 'I couldn't find the doctor [despite wanting to find him]'?
Hmm. "Nem tudom megtalálni a doktort." can include both my own defects and/or other circumstances while "Nem találom a doktort" simply states the fact, nothing else.
Okay; so English has a volitional distinction (cannot find/do not find) that Hungarian lacks? Whereas the Hungarian distinction is strictly between able to find/happen to find? Sorry for all the questions!
"find" is a stative verb in English and is not usually used in continuous tenses (am finding, was finding, ...). Instead, we use it in the simple tenses (I find, I found, ...).
Perhaps because by its nature it's something which happens very quickly - you look for something for a long time, and then, suddenly, you find it.
And in the negative, we usually use "I can't find ..." in the present tense rather than "I don't find ..." or "I am not finding ...". In the past, "I didn't find ..." or "I couldn't find ..." are both possible, but I think "I couldn't find ..." is more common.