So here is the situation:
I get internet if I connect my lappy directly with the router, but not over the switch. Other computers also get internet over the switch.
I tried re-booting both, router and switch.

On my end I use archlinux and, now, NetworkManager, but it didn't work with dhcpcd either.
Any ideas how to fix it?

Archlinux uses ip addr instead of ifconfig.

wat, the issue just magically resolved itself

Modem implies dial up.
A router is merely a bridge between networks. Dhcp etc. are something else that is built in most routers though.