@BawAsuk: I don't think there is hope, as the HP support keep on wanting to shift blame to the router.
@8Lives: Have used SMC, which in itself was not very good and at some point I even thought it was the problem. Now have a Netgear WNR2000, which works a dream with all my devices (except the printer). I can possibly also test TP-Link access point, but I am dead certain it is not a router problem and I am not in the mood to reconfigure my entire network AGAIN. Even if there is some obscure router config which fixes the problem, it should not be this way and HP should fix it.