Are you able to gain cores? I bought The Elder Scrolls V: Skyrim without looking at the specs. I need at least a dual core processor but I only have a single core processor.
You have to buy another CPU, most certainly a new computer because you would have to exchange a lot of other parts of your system to fit the new CPU.
You'd have to exchange your Motherboard, which holds the CPU in a so called socket. These change with each new processor generation. You'd have to exchange your RAM and graphics card as well i guess. Your graphics card will probably still use an AGP-slot, although there might still be newer boards with such a slot. The performance of the card is probably not enough for Skyrim.
But I am just guessing here, fact is: More cores only with a new CPU.
In your case, there is no way to gain more cores. Walter Maier-Murdnelch explains rather good what should be done to be able to play Skyrim.
I want to add though: it is in fact possible to get extra cores with some models of processors - if you are lucky. some AMD Phenom II models for example, are all 4 core models. The models that ship with fewer cores just have a few cores disabled. Often these cores are also defective. But here comes the lucky part: it is possible that the disabled cores work just fine, and you can in fact enable them.