I have no idea how you would be able to find a graphics card that can handle Skyrim under 40 dollars. Add in the laptop requirement, and you are talking about something that is just plain impossible.
In fact, you might not be able to get your laptop to run it at all. Sorry dude, but you'd just need a new computer.
If you are going to get a new computer, I would get a PC. Laptops are portable and all, but they are really expensive if you want to game, and I was able to build a PC that can play Skyrim on ultra with no problems for around 550-600. It is quite an investment, but I think it is worth it. You might want to use this website to find parts too.
http://pcpartpicker.com/
I didn't use this when I made mine, so you could probably get the same build for cheaper.
Also, don't be overwhelmed by the idea of having to put together a computer yourself, don't be. It's like big legos.
EDIT: I researched your card, and found out that it actually isn't a card at all, but integrated graphics. What integrated graphics does is borrow from your RAM in order to do things.It might be possible for you to change it in the BIOS of your laptop (Like video buffer size or something like that) but I wouldn't count on it. If you can change it, you could possibly get more RAM for your laptop, and then increase it. This is the exact problem that I had on my laptop a little bit ago, so good luck. About 4Gb of laptop ram is about $50, so that is a lot closer to your budget, but I can't guarantee it will work. It all depends on the computer. And even that will not make the computer work like a charm, but it should be better.