I have been seeing a lot of XP machines with issues after installing SP3 as of late, The most common issue I have seen is SP3 installs correctly but there is the loss of internet connectivity or SP3 didn't install correctly and there are several issues.
For the internet connectivity issues check you network adapter properties and look for tcp/ip v6 and either uncheck or uninstall it that will usually fix the problem.
For the more severe issues where SP3 did not install correctly you may not even know SP3 was installed if your computer is set to update automaticly all you notice is you machine is just very slow no internet and other type issues crashes BSOD's check you system properties in control panel if it shows SP3 go to add/remove programs and find SP3 and uninstall this can take some time so be patient after uninstalled and rebooted the machine should be back to normal.
Hope this helps if your having SP3 issues