Boots up then shuts down windows critical error and goes back and off again

Not necessarily. This usually means an error somewhere in the critical operating system files. whether this is software problem or hardware remains to be seen.
Assuming that you will, sadly; not be able to access the operating system again, you can still access the files and get a back up using a hard drive adapter: http://www.coolmaxusa.com./productDetails.asp?item=CD-350-COMBO&details=overview&subcategory=converter&category=converter
This does involve having another pc to load the files onto. Once the data is backed up a format will indicate if its a hardware issue but hopefully the format will manage any bad sectors. Once the format is complete the hard drive can be placed back in the laptop and an OS can be reloaded.
This all is if you wish to backup, you can just load in an OS cd/recovery disk and let it format the drive and just Install rewriting over any data and formatting around any potential bad sectors on the drive.

Hold the power button until the computer shuts down.
Restart and press F8 key repeatedly until you get a start up menu.
Select safe mode from the menu.
After the computer boots up, and you are at the desktop, go to my computer and select properties of the C drive (your system drive). Select tools from the tabs, then defrag. When defrag finishes, select check drive for errors and select the box, to automatically fix errors, and then ok, and yes at next window, allowing the computer to schedule the error check at next boot.
Reboot and allow computer to scan the drive.
After it finishes, you will continue into windows. Allow windows to boot. After it finishes, attempt to shut down again.
If it works, you fixed it. If not, you have a driver or program that will not quit, and you will have to research further to find out what is running and why it won't quit.

You have a rootkit virus, the only answer is reformat the drive and start fresh, sorry.
After a fresh install is done immediately install service(can be downloaded free from microsoft.com) pack 3, because sp2 is vulnerable to a host of trouble.

Your Operating System probably corrupted due to unexpected power failure or any other reason. You may have to setup widows again.

Before reinstallation take backup of all necessary file in a separate Hard Disk from your (C: ) Drive , existing desktop , my documents , share folder, etc. to do this you have to connect you Hard Disk with another workable PC.

After taking all necessary backup, setup Windows freshly and it is recommended to format C drive during fresh setup.

Try to start in safe mode and then when it finished loading shut it down again. Boot again it should boot to windows if it not, maybe a corrupted files or some files are missing.

On the windows boot screen you should be getting choices for safe mode, safe mode with networking, etc ...

Select "Disable automatic restart on system failure'

And let me know what error message(s) you have ... write it all down

no computer is trash when you are dealing with a software issue.

boot up and tap on the f8 key... when you get to that screen... choose safe mode... if it successfully boots.... go to start menu... and restart again... it should boot... if it wants to do the update let it.... if still nothing.... f8 again and choose last known good configuration

Robert

The most common shut down problem is that the system will reboot rather than shutting down. In most cases, the reboot is triggered because Windows XP is designed to reboot after a critical failure. To stop windows from rebooting in case of a failure, you need to take the following steps:
Right click on My Computer, Select Properties, Click on advance tab, Click on Settings under Startup and Recovery, Uncheck the option Automatically Restart under System failure, Click Ok twice and try to shutdown the pc. If it shows any error code then let me know

no i have not

It sound as if there is a system file error. If you havent already, try booting up in safe mode (F8) on start up and when and if it allows you highlight 'Last known good configuration' and hit enter for a restart. If still nothing you need to insert your windows installation disc and hit enter when prompted. This will run a file installation, but not a format and when the files have installed you will have the choice to install windows or repair; select repair for system file installation.