If your computer is as old as you claim it is, might need to buy a better computer to run Skyrim because if that computer doesn't at least have a dual core processor with 2.0GHz or above you're going to have a difficult time. Not only that but 2GB of RAM is pretty much the bare minimum. Also with the power supply possibly being a relatively low wattage you're going to be running a very low-key GPU if you can find one that is compatible. In reality it will not be pretty.
So buy a new computer if you really want to play Skyrim.