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Because I first thought the problem was net.eth0, the thread subject still says so, but this is wrong. The subject should read "sshd", can someone change the it?
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I'm making a small home fileserver. Because the old network didn't work with wake-on-lan, i bought a new one. After a big problem (udev renamed eth0 to eth1) with getting the new network card to work (at least it should work) i have a new problem.

In the boot sequence, after starting sshd, the system hangs. I think it's a kernel panic, because the LEDs on my keyboard are flashing, although there is no output on the screen.

When I start Gentoo with the "interactive mode", and skipping sshd, it boots like it should. I think this has something to do with the change of the network card, probably because of a change in the mac address.

I have not seen a problem like this before, it's probably not very hard to fix, but I can't find any solution on the internet. Henge that it's not a solution to "just don't use ssh", because I need it to use the server.

Try

grep -r eth1 /etc/ssh/* :-D

I tried
grep -r eth1 /etc/ssh/*

and

grep -r eth0 /etc/ssh/*

But none of them gave any output

I removed the key files, and executed "/etc/init.d/sshd start". Sshd generates a new RSA key, however, after showing the RSA random art (it only generated the first key) my system hangs with no errrors and blinking keyboard LEDS.

Configure it. There's a conf file that you can find examples for online. At least you know what's going on.
There's usually some foreground mode where you can start it on a terminal and it pumps out what it's doing, so you can catch the errors. This is what my /etc/ssh shows

bash-3.1$ ls /etc/ssh
moduli ssh_host_dsa_key.pub ssh_host_rsa_key
ssh_config ssh_host_key ssh_host_rsa_key.pub
ssh_host_dsa_key ssh_host_key.pub sshd_config