That unexpected guest was rather rude - but before we can get the power core back, repairing the emergency generator would be a sensible thing to do.
Unlike normal walkthroughs, in Nice Game Hints you can select just the puzzle you want hints for. Here are listed the puzzles for "Part 2 - How to repair the emergency generator" in Primordia. The guide you choose only contains information about that puzzle, reducing possible spoilers for other puzzles.