Problem Description:
HP pavillion a1250n computer in reboot loop after Sp3 installtion.
Troubleshooting Performed:
Tried to go to recovery console to do a system recovery. Was unable to proceed because the system installation was customized by HP and it was safe not to proceed without proper knowledge of the installation.

Action Plan:
First, the system will have to be brought to a bootable state without having to reinstall the OS. It can be done in recovery console. Best guide will be HP technician because they have customized recovery options.
Second, there are two log files Windowsupdate.log and svcpack.log which we need to check for incompatibility errors.
Then we can come to some definite conclusion whether Sp3 will be compatible or not and try to install it again.

The following are the links which you can go through.

Check http://support.microsoft.com/kb/297185 for 0x000000ED error.
Check http://support.microsoft.com/kb/888372 for known issues relating to AMD processors.
Check http://support.microsoft.com/kb/936929 for steps to be SP3 release notes.
Check http://support.microsoft.com/kb/950717 for steps to be taken for Sp3 installation.
Check http://support.microsoft.com/kb/946480 List of fixes that are included in Windows XP Service Pack 3.
Check http://support.microsoft.com/kb/950249 To uninstall Sp3.