Starts to boot up then boots back down.

Make sure you have a bootable windows 7 dvd. You most likely have just the upgrade version or (a poorly pirated one.) Try installing the 64 version from the windows and see how it goes from there

yeah ..you have to disable the power saving mode..This is the only thing related with the battery usage that may disable the cursor..o r..just reinstall the touch pad..
to do that download its driver and run it into computer ..
here is the link
http://h10025.www1.hp.com/ewfrf/wc/softwareCategory?cc=us&dlc=en&lc=en&product=3795238&
just select eh operation system and download the touch pad driver..
or go to control panel ..open the touch pad icon ..and in there select default settings ..or enable the cursor again ..if it is disabled..
if this is not working ..try reinstall it like I said ..It always starts a clean installation from the factory settings ..
Avoid hibernate it ..cause will always preserve the last settings ..just close it proper each time ..this way it will boot and recognize devices each time from the start ..

It is likely due to overheating. I would leave your system for a bit to allow it to cool down. When you start it, prop it up from a flat surface a bit simply by putting a pen or a small article to allow for some airflow under it.
Usually a laptop not booting and shutting itself down is related to a hardware failure, low battery, or safety shutdown in case of over heating.
Give this a go, Let the laptop sit for 10-15min while off. Then unplug the laptop and remove the battery. Then plug it back in without the battery. See if it boots. If it is still shutting off. Contact the manufacturer for support or a local technician. -Ravi Shanghavi

Uninstall the driver and then reinstall. make sure the drive is not connected until the driver is installed.

check battery power. Lots of times laptops won't boot if the battery has gone down to low. Probably has just enough charge to turn the machine on but not enough charge to boot the machine.

The backup battery connects directly to the logic board. From the symptoms you are describing (rather clearly, thank you), it seems apparent that your logic board may be faulty.
There are two more things you can try.
1) Reset Open Firmware: Unplug-replug your backup battery, then boot the system holding down Control-Option-O-F. Your machine will boot into Open Firmware. Type the following commands, pressing the "return" key at the end of each one:
reset-nvram
set-defaults
reset all
Your machine should restart at this point. If it starts successfully, you should be done. Otherwise,
2) Reset the Power Manager. Turn the machine all the way off (no power). Simultaneously press Shift-Control-Option-power button, then release. (Do not press the fn (Function) key during this sequence.) Wait five seconds, then press the power button. If it starts successfully, you should be done. Otherwise, you will need to see a man about a logic board, which is probably not a cost-effective repair on a 1GHz G4.

Have you tried pressing F8 at boot time and booting in "safe mode". Then you can think of a solution.

the highest water fill cycle for your waher is the clean cycle.it will fill up with 2x the normal amount of water in this cycle than any other.look for a cut or wrinkle in your door boot(grey rubber outer ring that seals between door and boot)if you find one,only fix would be to replace door boot.also clean inner door glass that comes in contact with door boot ring,any hard water build up or sediment(dog,cat or human hair)will break the seal and allow it to leak.good luck

thanks for your reply i have replaced the battery with a new one and the same problem still exists... why does it not boot from power button?

I have seen this problem before, after booting to the external monitor go into the display settings and try setting the resolution to 1024 X 768 and the color settng to 16 bit or preferably 32 bit. If you can do this, then shut down the laptop remove the external monitor and try booting on the LCD display. BPCS