móc or umieć

Should you use nie umiem or nie mogę when you can't do something, but it may or may not because you are doing it wrong?

I would say nie umiem if I didn't have the skills to do something

I would say nie mogę if it was impossible because parts or tools were missing etc. or the machine to do the job was broken

What do I say if I am not sure if it is me or the machine that is the problem?

I am using something for the first time, I shouldn't need to learn a skill to do this task because usually things like this are intuitive but I still can't do it. It could be me or the machine.

You use nie umiem only in situations where something can't be done solely because of your lack of skills.
Nie mogę can be use when:
-something cant be done because of you
-can't be done because of some objective reasons, independent, unrelated to you.

You can say 'Nie dam rady tego zrobić'.

Nie mogę. = I can't (am not allowed)
Nie umiem. = I don't know (can't____ because I don't have the knowledge/skill, hence the ability!)
Nie potrafię. = I can't (am physically unable)

my take is:
móc - to be able to, like physically
umieć - know how to, like learned knowledge

Thanks for all your help.

Czym MOGĘ służyć? = How can/may I help you? ("With what MAY I serve?")

UMIESZ po niemiecku też, Gochu? = Can you speak/Do you know how to speak German too, Maggie?

Niestety nie POTRAFIĘ się spotkać z Tobą dziś wieczór. = Unfortunately I'm unable to get together (with you) tonight.

Dzięki Lyzko

That's NOT right.
Niestety nie mogę sie z Tobą spotkać dziś wieczór (wieczorem).Potrafić is used in regard to skills very similar to umieć and often interchangable e.g Potrafisz prowadzic czołg?

Tak, ale jednak NIE "Potrafię po niemiecku.", lecz "Umiem po niemiecku."

Either but an educated person like me would rather say Potrafię mówić po niemiecku instead of Umię mówić po niemiecku.Don't argue my man,you are not nat naitive speaker.

Umiem ofc not Umię.Sorry.

To nie problem, panie profesorze! "Umię" jak "Rozumię"??:-)
Myślałem może pan pisze tu po ukrainsku
LOL

Ukrainians use cyrillic.Powinien pan to wiedzieć panie Lyzko.

this is plain wrong - as someone already stated POTRAFIć has everything to do with skill


potrafić can be contrasted with być w stanie - Potrafię rozwiązywać takie zadania ale teraz nie jestem w stanie. I can solve such mathematical problems but I am not in the shape to now. (sometimes 'to able to' can well replace 'to be in a shape to' I think)

Już wiem, jak pisze się po ukraińsku. Ale "umiĘ" jest ukraiński, nieprawda?

ukraiński doesn't have the nasal vowels - I don't know about ukraiński - in Russian it's umieyu (in Polish transcription of of Russian it's umieju if it helps)

No, dziękuję! Porządku:-)