[CAUTION: I am not a teacher:take the advice and or corrections offered in this post at your own risk.
If you doubt the information, please get a qualified opinion from one of the teachers on these forums.]
The infintive works like a particle, it can't decline and as you may have noticed, the sentence changes around it to modify the specific meaning.
I hope to see him.
It was my wish to see him.
It has been my dream to see him.
Presented kind of "backwards" and in a passive construction as you write it, it seems more confusing.
We have to ask:what is "to see him." in this sentence? It is inconsequential and can be removed from the sentence, but remains as a dependent component to provide detail, but the verbs are "hope", "it was" and "It has been" respectively.
He is believed to have been kidnapped.--The verb is "is believed to have been"
It is believed he was kidnapped.--The verb (in the main clause) is "was".
I recognise that my answer here still leaves some things unexplained, but this is a little out of my depth, can anyone else shed more light on it? (I would even like to see the initial poser of the question attempt it)