If you meet the MINIMUM hardware requirements(at the bottom of the TF2 store page) then your computer is simply misconfigured. Get a local nerd to help sort out your startup programs and services. If you don't have adequate hardware then you're out of luck.
And if you're seeing pink triangles and checkerboards everywhere then your video card doesn't have enough video memory to load all the 2D textures. If you have a desktop simply upgrade your video card. If its a laptop you may have to get a complete replacement as the video chipsets aren't replaceable/upgradeable. DO try upgrading your video card drivers before you decide to throw anything out.