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
http://support.microsoft.com/kb/947366

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
http://support.microsoft.com/default.aspx/kb/929135

I see lots of recommendations here for programs like -

Malwarebytes' Anti-Malware
http://www.malwarebytes.org/products/malwarebytes_free

A certain amount of logging is produced during SP1 installs, these may contain helpful clues.

See what any logs can tell you.
http://www.windowsbbs.com/windows-vista/77096-startup-problems-after-downloading-sp1-vista.html

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.
https://support.microsoft.com/oas/default.aspx?ln=en-us&prid=11274&gprid=500921



 

Try running ChkDsk to check your drive for errors. Right-click your Drive icon/ Properties/ Tools/ Error Checking.  Try it first by not checking either box (Read-only mode) to see if it flags any hard drive or file problems.  If it does, start by ticking both boxes, in any further rerun.

The hard drive manufacturer will have free diagnostic software that is bootable, or that  may even run from within Windows, that will thoroughly check the condition of your hard drive.


How to Use the Memory Diagnostics Tool in Vista
http://www.vistax64.com/tutorials/65361-memory-diagnostics-tool.html
 

Service Packs are cumulative.  Why would you even bother trying to install SP1?  Better to go right to SP2.

That doesn't "fix" the problem here, but it saves turning right around and installing another big patch.

Nevermind.  I see that this isn't true of Vista/2008 Service Packs.  My mistake, it's been too long I guess.  I must have been thinking of XP Service Packs.