After fiddling around with alternate cables and chargers, I discovered the problem. This might be applicable for other users, so I'll post it here as a reference.
The sliding prong (they are exchangeable between different countries' outlets) had come loose, but just a tad. It wasn't visible. First after deciding to try the Asus charger with a Samsung tablet, to see if it produced electricity at all, did I discover that it wasn't fully attached. Since I now could charge the Samsung tablet using the ASUS charger I tried it again on the ASUS Transformer, lo and behold it began charging. However, notice that the Samsung charger didn't produce a charge, so it seems to be important that the correct charger is connected. Hence, if you run into charging problems, start with the sliding prong.