Yeah, カラオケ refers to karaoke equipment and karaoke box (a small room containing karaoke equipment) in your example sentences, respectively.
カラオケにいきました shows that the speaker was in another place before going to the karaoke box, and then went there, i.e., they went to the karaoke box from another place, whereas カラオケがありました means that they were already in a place (in a saloon, friend's room, etc.) and there was a karaoke equipment there. Thus, the situation where those expressions are used is different as same as "I went to a karaoke (box)" vs. "There was a karaoke (equipment)" in English.
Another nitpicking; speaking strictly, なにもうたいませんでした means "didn't sing anything/any song".