I have XP fully up to date.

The other day just finishing working on my laptop, I put it on the table. The plug came out of the AC/DC Adapter and the computer when dead.

Tried to reboot it No luck
Tried to start in Safe Mode No Luck
Tried to go back to last good start up No Luck
Tried to boot from CD No Luck
Tried to boot to safe mode form CD No Luck

But I have now reformatted the hard drive, and reinstalled XP and it is working OK.

What happen, why would it not restart?

No way to tell now, since reformatting removes any evidence at to what was wrong, or how keep it from happening again - my guess is when you lost power suddenly, the hard drive boot sector became corrupt. I suspect you could have done a XP Repair Install instead of a format and reinstall, but no harm done, assuming you had your data backed up, and you have now fully updated your system, and setup a good security defense.

Was the battery installed and charged? I would wonder why the battery did not keep the notebook running. How did the plug come out? They don't normally just fall out. Was it yanked out?

Sorry for not getting back to you before.
The battery is U.S, I have to run it off the mains, I have looked a buying a new battery but it was very, very expensive. The plug of the mains lead into the power pack was loose. I have now replaced it with a new one.

Thanks for follow up.