The correct answers are I finally got the new intern to compile the quarterly reports., I had the new intern compile the quarterly reports., and I got the quarterly reports compiled by the new intern.

When using active causatives (focusing on who is doing the action), have takes the bare infinitive (have someone do something), whereas get takes the full infinitive (get someone to do something).

When using passive causatives (focusing on the action being completed), both verbs use the past participle (have/get something done).

Therefore, "had the new intern to compile" and "got the new intern compile" are grammatically incorrect mixtures of these rules!