iBook M9419LL/A
Screen first turned black with white horizontal lines,
now only the fan will start up when power button
is pushed.

What may have died or hopefully come loose?

This 14" iBook from early 2004 is having video issues

Since it is "Out of Warranty" because of its age, it could qualify for a Flat Rate Depot repair of around $300. Have them plug an external monitor into it and see if the video is not working there as well. I'm betting it isn't. Depending on the actual "Date of Purchase" it may be considered "Vintage" by Apple.

Next time give us more info than a model number

How much more do you need, Mr. Dave?
You have MacTracker just like I do, the specs are all there.

Video issues may mean what specifically?
Loose cable, dead cable, melted cable, what?
Why is the fan running constantly when we try to power up,
and will not stop until the battery is pulled out?

Wow, the exact problem that is ocuring, with a possible solution:
iBook G4 Black Screen of death with a loud fan

I was going to say the issue is with the MLB (logic board) and I believe your link confirms that diagnosis. Should they wish to attempt the "fix" mentioned in the article, tell them to be careful not to touch the logic board anymore than needed. An Electro-static Discharge can render that unit completely useless.

Whoever the fixer is, here are some home grown static precautions.

1) Work in a non carpeted area. I like to find a tile area best to work in. Reduces the chance of static.

2) Buy a static strap and follow the instructions for proper grounding. If you don't have a strap, make sure to touch some metal to discharge yourself before starting work on the laptop.

Good Luck Bucko!