You may have to disable all anti-virus and anti-malware software before trying to install SP1. If you do disable them you should disconnect from the Internet until the install has finished.
It is also a good idea to delete all unneeded files from you PC with a program like CCleaner click here defrag the hard drive and run checkdisk on the drive before installing any service pack. It may seem a lot of work and bother but it is well worth it.
Were you able to download the Microsoft fix point 5 in phono's advice?
"5. If the installation still fails, download and extract the KB947821 update from the Microsoft Download Center. The Windows6.0-KB947821-XXX.msu file will ensure that the computer is ready to be updated. Then try to install SP1 again."
And if so did you get an error message with that as well?