Because of some problems, I decided to reinstall Windows XP. Everything went smoothly, until I got to the network connection.
No connections show on the Network Connections page, and the network card has a question mark icon in the Device Manager. Checking the properties of the network card, it says no drivers were installed, so concluding what was wrong wasn't too hard.
It's a D-Link DFE-530TX, so I went to the site of D-Link for a driver. It said the driver was integrated in the installation cd of Windows XP, but I found a downloadable one in the end. I installed it, and it asked for my opperation system, and Windows XP wasn't an option. I then chose Windows 98, figuring it couldn't harm, and installed it. Nothing happened. Trying three more versions of the same driver, on different locations, I finally found one that didn't make me choose between different OS. That didn't work either. So now, I don't really know what else I could do. Does anyone have an idea? Thank you.

Oh, btw, until I can fix the problem, I have the new XP dualbooted with the old XP. The old one has no problem whatsoever with going on the internet, so it shouldn't be a problem with the hardware.
Is there perhaps a way to get the driver from the old XP, to use it for the new one?

Yes
Use DriverGrabber on the old one http://fileforum.betanews.com/sendfile/1170699160/1/DriverGrabber.zip

Then copy all of the found drivers to CD or USB flash

Done.

That card uses either a Realtek 8139 or VIA Rhine chip (just look at the card to be sure) and those drivers are indeed included with Windows XP. Choose to install drivers manually and force one of the abovementioned. (Or, go to Realtek's website and download their 8139 driver package)

Oh, I like DriverGrabber and no one uses it :(

It works again. Thank you both for your help.

Argh! What was the solution?