What have you tried, otherwise we will be repeating suggestions that you don't want to do?
How to troubleshoot Windows Vista and Windows Server 2008 service pack installation issues
Basically SP1 needs a reliable and clean machine to successfully install into, and one that is fully updated, especially with all the Reliability updates and the System Update Readiness Tool.
How to troubleshoot a problem by performing a clean boot in Windows Vista or in Windows 7
I see lots of recommendations here for programs like -
Malwarebytes' Anti-Malware
A certain amount of logging is produced during SP1 installs, these may contain helpful clues.
See what any logs can tell you.
Remember the basics like disabling (temporarily) security programs like Anti Virus and Defender, running as Administrator, (Elevated via right-click) if you have a setup file to click on, turning off (temporarily) UAC, disabling startup programs (temporarily) via msconfig, etc.
Installing Service Packs have always required a clean system to guarantee success, it is at this time that old forgotten tweaks and installed security programs come back to haunt you. A Format of the partition, a clean install of Vista, followed by SP1, is one sure way of achieving a successful update when every other means fails.
Microsoft offers free support for SP1 troubles if you want to contact them.