Solved it! That was a tricky one to find, though, thus I would like to share the solution here: it turned out to be a faulty Ethernet-cable. In fact, I noticed in the logs of my Firewall that there were DHCP OFFERS going out, but no ACKs were comming back. I used one of those RJ45-wiring testers on the cable in question, which however displayed all 8 wires to be connected. Therefore I turned the option of a faulty cable down at first.
Only when I tried getting a connection through that very cable using my MacBook and didn’t get one I got my digital multimeter out which eventually showed a very high resistance on one of the wires – apparently still conductive enough for the simple cable tester to show the wiring to be ok.