Check your logs in the event viewer Nekro. I'm still trying to figure out why my Server 2k3 box refuses to work with my Gig nics. It will start a transfer then basically hang the client pc until I can finally kill the transfer. If you look on the logs on the server it's flooded with error messages.
The Intel Pro 1000 are really nice nics. The ones you linked would work well because they are PCI-E. If it were just a PCI card I'd be afraid of the interface bottlenecking your connection.
Also, did you check your settings for that realtek nic and make sure anything like TCP/IP offloading was turned on? Your usage seems quite high. I have a linksys EG1032
that's in a little AMD athlon 1800+ 1GB ram pc running Server 08 and it can get to about 50% network usage before I run out of CPU. You probably have 10x the amount of CPU in that pc than what mine is, so it seems like something isn't setup right.
EDIT: Also look for Flow control for both TX & RX, and Checksum offloading.