I've been having a lot of difficulties installing Chrome on my desktop, I have Windows XP with SP3. The setup program starts and then exits within a second. I can see in Process Viewer that it's accessing a lot of files and registry keys before exiting
The thread Can't install Chrome on Windows XP SP3 discusses this problem.
First, ensure that you have the latest XP SP3, rather than a release-candidate (RC).
Then, download Chrome setup, reboot in Safe mode and install.
If this doesn't work, you could follow the other rather convoluted directions in the above link.