The Tradëscan Codex

"Me", like "Mom", is the object of want, hence it is in the accusative; and it is not the subject of "to go" (even though you are the person who will carry out the action) because "to go" is in the infinitive and therefore cannot take a subject. However, this is one of those areas of syntax where English is in the process of change - it's becoming increasingly common for speakers not to inflect the pronoun in situations like this, where the pronoun is paired with another noun ("Do you want Jim and I to help you?"). I think it only applies to the first person pronoun, though ("Do you want Jim and she to help you?" is clearly not acceptable) and is probably developing by analogy with "X and I" in the subject position (like the Queen always saying "My husband and I").