I see this time and time again, someone buys a used computer for themselves or a family member and get ripped offer because they did'nt know of some obvious things to look for.
In addition to what I mentioned in the video here are some KEY things to look for:
Dents and dings in the case
Heavy collections of dust and dirt in the system
Try to turn on the system, if they won't let you do it - you don't want it.
Make sure everything shows up in device manager by Right clicking on the My Computer icon and going to Manage and then device manager. Make sure there are no yellow triangles or exlamation marks. Red X's mean something is disabled, and is not always an issue.
Be sure there is a Windows product key on the system case. This is a sticker that has 25 characters and will say "Microsoft Windows" on it. Do not be fooled into thinking a Microsoft Office product key is the same.
Check the hard drive size and make sure it is not an abnormally small amount
Ask if there are any restore disks with the system.
Know what operating system it is running, do not buy anything older than Windows XP for internet use.
Performing these few checks can save you alot of time and trouble when buying a used computer.