The minimum requirement for .NET Framework 3.5 on Windows XP is that SP2 for XP be installed.
If you believe the system in question meets that requirement, post the link to the download you tried to install, and provide complete logs as follows:
Please collect your install logs with this:
http://www.microsoft.com/downloads/details.aspx?FamilyID=E0DA314F-6216-4A18-BC6B-7D29CF83AF20&displaylang=e&displaylang=en
After you run Collect.exe, you'll find vslogs.cab in your %temp% directory. Please upload vslogs.cab to a public site, like SkyDrive, and post the link here.