Advice on diagnosing routing problems?

I can see some of the net, but not other bits. On Friday I couldn't connect to BT Yahoo webmail either at work or home, but yesterday I could from work but not home. I upgraded the router firmware at home (on the grounds that it wouldn't hurt, though its not as if I'd changed anything recently), and then could connect. But there are still sites I can't ping.
( tracert output for reachable and unreachable sites )

( ipconfig output )

( router table )

Any suggestions on finding the problem?
(The home machine with a Linux installation only has an unsupported wireless card.)