Well, beats me, but all of a sudden it works. Last night still nothing, this morning I thought to try another few options but before I'd do that I pinged again (like the many times before) and now the computers could see each other.
Strange thing though: the laptops ip-address had changed from, say, 123.456.7.15 to 123.456.7.16...
And the lease couldn't have expired - that's put on 48 hours.
My impression is that my provider has done something with the firmware of my router this night, because other people were having issues with it too.
So (and that's why I wanted this home network to work in the first place): MC Server works again!
Thanks to all for thinking with me!