Toshiro, in my thread there is a list of GFX cards and their ratings. Since the list of your components says only "Intel GFX" it is hard to figure out exactly what you have. Usually stock computers will have what is called "integrated graphics". Which means the graphics chipset is built integrated into your motherboard.
If that is the case, from my extensive reading, I have learned that any integrated graphics is pretty much a "no go" on Skyrim. Skyrim needs a moderate to higher quality dedicated graphics card to run it. This is partly due to the nature of integrated GFX using your system RAM and processor to calculate graphics functions. Which means your processor and RAM resources will be stressed.
This is why a dedicated GFX card will actually have RAM built on it as well as a GPU. Graphics Processing Unit which will function to carry out your graphics calculations. If a system processor can be thought of as the human brain, think of a good GFX card as like a "Graphics Brain" which is there to concentrate on the graphics only.
I'm intermediate skill level at best, with tech stuff. I understand a lot of concepts but have not actually done much myself. You might take your Laptop to a PC shop nearby your house and ask them specifically "If they can tell you what kind of graphics card you have or if it is integrated into the motherboard." Or you can ask how to do it yourself in forums like this or Tom's Hardware that FinalChrono told me about. There may be diagnostic programs you can use to tell you as well. This can be helpful to let you know where you stand currently, in order to get you to where you want to be, which I assume is having an enjoyable experience playing Skyrim.
As your machine sits now it looks like it may have the bare minimum requirements and so, based on my 2 to 3 hours of research on comparable machines, I would say you would not be able to run Skyrim well on that PC.
1. I base that off your processor being the bare minimum requirement.
2. Plus the unknown GFX card, which, if it does not specifically say we can assume it is integrated GFX.
3. And if your system only has 2 GB of RAM you will need at least 4 GB. (find that out too)
4. Ahh yeah and as I read the description of your Asus F80Q Laptop I see that, due to the 32 bit Operating System, your OS will only recognize 3GB of a 4GB setup. Which means you will lose 1 GB of memory b/c of the limitations of the 32 bit OS versus a 64 bit OS. That will be a problem as well.
Sort of bad news i know, but good to know where you are in order to get where you want to be.
Although I've been out of PC gaming for a few years, I have been doing research since playing Skyrim at my cousin's house and loving it. You might check out the thread I originally posted in too. As it has some tech info straight from Bethesda that might be of help to you.
http://skyrimforum.com/threads/double-checking-my-incoming-hardware.2210/
Good luck! I know how you feel b/c this is all i want for Christmas! Hehe.
~Matt