That is a very difficult question to answer. CPU cores have changed incredibly over the years in power consumption, the invention of the battery powered laptop made this a necessity. Depending on the generation and speed of your CPU you are going to draw more or less current. Depending on how many hard drives, or how hard working your video chip is, etc etc, the draw can be quite different. Intel just released a new CPU called the ATOM that is aimed at low power consumption, here are a few things they say about it:

Get a new range of power-efficient devices with excellent performance enabled by all new hafnium-infused 45nm high-k silicon technology

Increase energy efficiency in smaller more compact designs with a thermal design power specification ranging from less than 1W to 2.5 watts for mobile devices

Extend battery life in select devices with an incredibly low idle and average power allowing the device to stay powered on while also conserving energy

So, you can see here that technology makes a difference, and unfortunately I can't really answer your question as a result. If you know basic electronics you could wire up a simple circuit that would pass the current you computer draws through an ammeter to measure the amperage draw, from the average current draw you calculate power consumption with Ohm's Law:

Power = Current X Voltage

That would give you Watts. 1000 Watts drawn for 1 hour is 1KWH, so you can use the Power consumption calculation you made for your PC in watts, and figure from that how much running your computer would cost you for one hour. Going further, you can get the cost per KWH from your electric company and calculate the cost in dollars, but this is not always possible because bills are often calculated with the first XX KWH's billed at one rate and then the rest of the KWH's above that limit billed at a second rate.
Hope that was somewhat helpful and wasn't too confusing...
Irie