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Oh, I do hope this question isn't from a quiz. If so, it is poorly formed and ambiguous given the sentence you have to work with, and you have my sympathy. But let's have a go at it. We'll assume "main subject" means the subject of the main clause, which is "they became interested in determining the behaviors associated with each status". (The rest of it, "Once researchers were able to identify rejected and neglected children ..." is a dependent clause that modifies the rest, but you should be able to ignore this for the purpose of this analysis.) So the pronoun "they" is the subject of the main clause, and so what may be called the main subject (although I have a sneaking suspicion they are after "researchers" instead). Similarly, the "main verb" can be identified as "became". Now, the bit that gives it away as a badly-formed question -- there is no object for that verb. "Became" is a linking verb, and it has a subject complement instead of an object. That complement here is the adjectival phrase "interested in determining the behaviors associated with each status".

What I call the core or skeleton of the sentence--I don't know what teachers or grammarians call it--is simply "They became interested." The first part of the sentence sets up the conditions under which the action occurred. The last part of the sentence modifies or explains the word "interested." But what is happening, what is actually going on is "They became interested." Thanks to James for giving the proper grammatical names for the verb, and for the grammatical function of the word 'interested." I realized it did NOT fit the pattern "subject, transitive verb, object."