Realtek 8111E Gigabit LAN not working
 

I just installed Slackware in a Dual-boot computer with Windows 7 running an Asus P8Z68-V LX. I installed all the drivers and everything Windows needed fine so it's not an internet problem. I'm now trying to download some graphics card drivers but the connection starts fast, but then quickly slows until it just stops. Any idea what the problem is?

Take a look at these two links detailing the problems your nic:

http://www.twm-kd.com/linux/realtek-...-ubuntu-linux/

http://askubuntu.com/questions/15796.../159031#159031

Basically, it appears to be a kernel issue; the driver provided in the vanilla kernel for this nic is actually designed for a different nic and only sort of works on your nic.
The above links discuss the solution, namely, downloading the proper driver module from Realtek then compiling and installing it on your system. I would imagine future kernels will correct this problem; apparently Realtek didn't get the fixed kernel module included in the current kernels in time. Alternatively, you could just throw another nic in your box, assuming you have an open pci slot on your motherboard. Almost all nics are supported by current linux kernels out of the box.