Hello ej and welcome to Seven Forums.
Have you tried downloading TF2 on another computer to see if it also lags or freezes? If it does it could be a problem with the download site rather than the computer.
Other factors that could affect the download include how much memory is installed (2GB RAM is considered the minimum for Windows 7 with 4GB being the sweet spot), hard drive problems like bad sectors, failing HD, etc., malware on the machine, and a whole lot more.
Here's a tutorial that covers how to optimize Windows 7. Some of the suggestions may not apply to your brother's machine but others will. Optimize Windows 7
And another Forum member created this checklist of maintenance tasks that should help any computer. Heed his warning about NOT using registry cleaners. Suggestions for Proper Maintenance