Skyrim is going to be a monster game and will need a quad core proc in order to really make it playable. Plus, depending on the age of the mobo, you may be on PCIe1, which will choke most modern GPUs on blockbuster games.
Time for a core upgrade: mobo, proc, ram, GPU, and possibly a power supply. Then later add more ram, a modern HDD/SSD, a 2nd GPU, and a ligger power supply if you didnt already.
If you have not been keeping up, be aware that new AMD chips are coming out 'soon', as are the new GPU lines for both AMD (Q4 2011), and nVidia (Q1/2 of 2012). Intel is also doing a chip refresh, but it is just for high end stuff and may not affect you. Their next mainstream processors will come out somewhere around Mar/Apr, which may be a long wait as they are not going to be much faster than current intel chips (though a lot less power consuming!)