Which describes how the pronoun is used in the sentence ? the first person in the door was she

If we are refering to 'she' (given there is no options), 'she' is used in the objective case, that is, the pronoun acts as an object coming after a transitive verb (able to take a direct object). However, I would have thought personally that 'she' should be replaced with 'her' – because wouldn't 'she' be a pronoun of the subjective case? Very open to suggestions and corrections :D

Polonius's statement was translated in modern english. i found it in a website that does analysis  and it goes like this:

" we’re doing this wisely and intelligently, indirectly, finding out things by roundabout means. that’s how you’ll find out what my son is up to in paris. you get my point, don’t you? "

his method of finding out the truth about his son is by  spying on him.   though it is a dishonest thing to do, polonius thinks that it is the best way to know what is true instead of asking his son directly about what he is up to in paris.