Hi, Johnny. Welcome to Apple Discussions.
It sounds like you're right on track.
It is usual for an iBook with a logic board that is going bad to work sporadically.
Keep an eye on your purchase date, and if you keep on having trouble, send it in. The
iBook Logic Board Repair Extension Program has a three-year cutoff date, so if you are having any problems at all with the logic board, get it sent in before that. The case number that you got today will help.
Keep your files backed up so you don't lose anything.
Good luck.