If the PC is from a big name manufacturer, I would see if it already includes diagnostics on a hidden partition.
Most hardware diagnostics run outside the operating system because they need direct access to the underlying hardware.
If the computer didn't come with any diagnostics check out http://www.ultimatebootcd.com/. Its a free assortment of different diagnostics.
There are diagnostics designed to troubleshoot Windows itself that run on top of the OS such as Sysinternals from Microsoft.
If you suspect a particular hardware component. Post a question with the symptoms and someone hear is likely to give you an answer.