I suggest trying a different browser, perhaps one that's specifically optimized for the laptop, or you could try updating to IE 7 - but personally I would suggest abandoning IE altogether for Mozilla Firefox - it's free, faster, more effecient, and just better in general. It also might work better on a laptop.
The only problem is that if you have no way of accessing the Internet otherwise, or no way to transfer the installer for Firefox onto your laptop, and can't manage to connect at all on your laptop, then how will you get the installer? In that case you could ask a friend to download the installer for you and burn it to a disc or mini hard drive or something.
If you try another browser and it still isn't working, it's probably a bigger problem with your internet connectivity, in which case I can't help you because I know little about internet connections in general, let alone those on laptops. (I don't have a laptop and I've never used one.)