Hi Altuz,
welcome to LQ.
I am not sure wether your card needs the 'e1000' or 'e1000e' driver according to
Intel download center -- I typed 82566MM in the search field and am still in doubt.
To check which one is loaded, 'lsmod|grep e1000'
Anyway 'e1000' is included in kernels for Slackware 12.0, but 'e1000e' is not (only included in kernels for 12.1 and 12.2).
To find out which driver you need you can check
this link
Also, if you issue 'lspci -k'' you will see information about kernel driver in use as well as kernel modules.
To make a long story short, if your network adapted is fairly recent, I would try Slackware 12.2 instead of 12.0 and see what happens
But still, if you determine you do not have the good driver you could follow Intel's instructions to install it if you wish.
If you think that you have the good driver and the module is loaded, the 'dhcpcd eth0' command should connect your computer. Check with 'route' where you should see two lines with eth0 under the 'Iface' header.