How do I make it so that after logging in as a normal user, "startx" and "dhcpcd eth0" are automatically executed? Putting them in .bashrc isn't a nice solution because those commands are executed with every new shell. Also I'd rather not use a graphical login because that lengthens my startup time

I've already changed the necessary dhcpcd permissions so that a normal user can use dhcp.

The following is based on the assumption that you're using Gentoo, as mentioned in your user id.

Is net.eth0 in your default runlevel? You can try
This will add net.eth0 to your default runlevel if it's not there and will do nothing if it is already there (except tell you that it is there). Of course, this will start the networking on boot rather than after logging in as a normal user, which I realize is not exactly what you were asking for.

Also, make sure that the entry for eth0 in /etc/conf.d/net looks like config_eth0=("dhcp") and that net.eth0 is symlinked to net.lo (to check, use: ). That has worked without much problem for me. And if I lose the network connection I just use the following to bring it back up:
I imagine to have startx executed you would have to be logged in automatically as well. Check out the following thread from Gentoo's forums for suggestions:
http://forums.gentoo.org/viewtopic-t...tic+login.html