Sure, I'll try.
The reason why this didn't occur to me is that I already ran a ISPConfig2 installation under the same control panel software successfully before.
But it could of course be a firewall configuration issue. Can't remember how I set it up last time. Yesterday I checked, realized I had only added a firewall rule for incoming connections, and added a server rule for outgoing ones.
That did not resolve the problem, unfortunately.
I am now trying to find out how to disable this firewall without deleting every single rule manually. Once I've figured this out, I'll try again and post back here.
Thanks once more for your time.