Need or needs with bare infinitive

The active voice is speech that places the subject first, followed by a verb, and a place/object. Therefore the correct form is subject -- verb -- object.

The passive voice is speech that places the object first, followed by a verb (tense and a gerund), and the subject. Therefore the correct form is object -- verb -- subject.

None of these sentences are in the passive voice, since I (the subject), always comes first in each of them.

Most of these can be converted from active voice to passive voice:

I saw a person repairing my car. The car was being repaired by someone.

I saw a person repair my car. The car was repaired by someone.

I saw a car being repaired. / I saw a car be repaired. A car was being repaired.

I watched a man solve the problem. The problem was solved by a man.

I watched a man solving the problem. The problem was being solved by a man.

I watched a problem being solved. / I watched a problem be solved. The problem was being solved.

Notice that none of these use I, mainly because I couldn't find a logical incorporation. I suppose you could say (and use as a guideline):

The car was being repaired by someone I was watching.

The problem was solved as I watched.

The sentences I saw a car repaired and I saw a problem solved don't make sense to me because the past participle is just by itself. I would include words to tie it together with everything else:

I saw a car that was repaired.

I saw a car that had been repaired.

I saw a problem that was solved.

I saw a problem that had been solved.

I also think that adding a comma, though strange, is acceptable:

I saw a car, repaired.

I saw a problem, solved.