(End of March 2010...)
This morning when I woke up, I found that again I had fallen asleep in the bed reading in the computer.
I tried to switch it on but I couldn't.

Everytime I pressed the button, all the LED lights became blue as usual but then less than one second later the computer switched off suddenly.

I was afraid. Maybe the battery was faulty, but it was plugged to the electricity.
I went to lessons thinking that I would have to find a place to repair it.

During the lessons I found in the HP website that the symtomps pointed that it needed to be repaired but with other symptoms you could do a 'Hard Reset' and it would be working again.

When the lesson finished I came back home quickly and I did it. And it worked!! :)

'Hard Reset' consists on:

1. Take out the battery
2. Unplug the AC cable.
3. Press and hold the power button at least 6 seconds.

I'm posting it because it was not so easy to find the procedure. Now I'm happy again :) and I wonder how many laptops that have been shipped to be repaired could have been fixed doing that... And how much did it cost to the owners :-(

BTW, I started some time ago a page in the ubuntu wiki to get everything working in this HP Pavillion model. It's still in construction and some bugs need to be fixed before in the kernel. I'm working on it.. :)
https://wiki.ubuntu.com/Testing/Laptop/Reports/HPPavilionTx2000es

Update April 10th 2010: hard reset is not working anymore, my laptop seems dead :(

Update May 4th 2010: I just saw my laptop inside its cover under my desktop and with a bit of sadness decided to try to turn it on. Luckily and enigmatically IT WORKS AGAIN :)))

Hypothesis:
It seems that some internal capacitors had kept charged. In fact, what Hard Reset did, was trying to uncharge them. One month later it seems that they got finally uncharged.