I keep a spare (old, clunky) Alcatel Frog in the cupboard for those moments when the Internet seems stroppy. Unplug the nice wireless modem router, plug in the Frog, log in, and see.
When it's not the ADSL down (happened a lot with the previous ISP, very rarely with this one) the act of swapping over and back seems to fix it.
I suspect sometimes that just waving the Frog in front of the "normal" device would fix it.