MY Dell laptop running XP will run in safe mode but shut down after 2 minutes in normal operation. When I start it defaults to safe mode but allows me to restart and comes up temporairialy in normal mode then shuts down.

When the System comes back on in Safe Mode, all unnecessary utilities are shut down or do not work, such as your speakers or the sound. If you open Safe Mode with Networking, than you are connected to a Network, but you still can only do a few tasks that Safe Mode allows. After you restart your computer and run it normally, than all functions will return to their normal operations, including your speakers and sound.

First make sure your fan is operating on your processor it takes about 3 mins for it to over heat and stop and shut itself down for safety to prevent burning up the processor.if its not this read on.
Also when you boot into safe mode then do a system restore to a date before the problem started. But first in safe mode run your antivirus scan to find something that is missed while being hid behind the operating system while functioning. Remember to rate my solution and leave testimonial this is how i earn my achievements here on FixYa thanks in advance

As soon as you can get it to run either in safe or normal mode, run CHKDSK/F as that will attempt to repair the hard drive errors.

try to run windows f12 boot format it should be runing on f2 this way you can go straight to problem then asked to run windows again after you restart .

1.Shut down your computer and start hitting F8 key (on the top line of the keyboard.) immediately (on the top line) up and down at least 20-30 times and choose "Last known Good configuration."

2.If this does not work, shut down your computer and restart the computer in the "safe mode with networking" option.
How to restart the computer in the safe mode with networking: As soon you restart the computer, start hitting F8 key immediately (on the top line of the keyboard.) up and down at least 20-30 times and choose safe mode with networking by using the up and down arrow key on the keyboard and hit enter twice.
2. If the computer restarts in the safe mode then, please follow these steps" a.Disable or unistall any anti-virus Norton Removal tool link: http://service1.symantec.com/Support/tsgeninfo.nsf/docid/2005033108162039 Mcafee removal tool link: http://download.mcafee.com/products/licensed/cust_support_patches/MCPR.exe
b.run malwarebytes and scan your computer. http://www.malwarebytes.org/
c.cleanboot the computer.Please follow the Microsoft Link: http://support.microsoft.com/kb/331796
Restart the computer: 3.If the computer does not restart in the safe mode with networking, then choose safe mode option only(like you shut down the computer, hit F8 and choose safe mode only).
If it restart in safe mode, try to restore the computer to previous date: http://support.microsoft.com/kb/306084
4.If this does not work then try to restart the computer in safe mode with commmand promt. http://support.microsoft.com/kb/304449
5. If this all does not work, you might have to repair your operating system. For window xp: http://www.microsoft.com/windowsxp/using/helpandsupport/learnmore/tips/doug92.mspx
6. You might you have to restore the compter to factory settings. Note: This will delete all of the data on the computer and your computer would be restore to the very first day or to factory settings. a For Dell computer, As soon as you restart the computer, hold down the Control key and start tapping(hitting up and down)F11 key immediately and folllow the on screen instructions. b.For HP computer: i)for xp as soon as you restart the computer,start hitting F10 key, ii)Forvista as soon as you restart the computer,start hitting F11 key, c. For acer: as soon as you restart the computer,hold down the alt key and start hitting F10 key.
7.If this all does not work, you might have to reinstall the operating system. Note:This would also delete all of the data. How to install window XP: http://www.microsoft.com/windowsxp/using/setup/winxp/install.mspx Note: After installing window xp or vista, you will have to instlal the drivers by using the Driver and utilities disk that came with the computer.
8. If it all does not work,it may a hardware issue: For Dell computer, run Dell dianostic: http://support.dell.com/support/edocs/systems/opgx620/en/ug/tools00.htm if you receive any error, contact dell support team.
I hope, this would help you.

I am no expert by a long shot but is the fan running in safe mode is it overheating and shutting down?

Try a system restore - boot to safe mode and restore it to an earlier working state.

solution 1: your system is running in safe mode..as directed previously,restart the computer and on 1st screen(dell) press f8 5-6 times...and select start windows normally and enter...and try installing the same thing it will wqork
if not..
solution 2) then click on start> run > type services.msc > click ok > on right hand side in the list look for windows installer> double click it >property window will open up..if its stopped/ start it and from start up option select automatic >click apply ok..restart the computer. IT WILL WORK..
cheers njoy

There is most likely a software and/or driver confliction not allowing your system to shut down.  Have you recently installed new software or hardware?