[Hampshire] Network problems

My modem/router died yesterday, so today I installed a brand new one.

I configured the router and then the three computers I currently have linked
up.

I am left with some weird problems.

On Tux, any ping works, Konqueror works (i.e. goes to a web address when given
one), but neither Opera nor Firefox will resolve.

On Dozy, all three browsers were working fine. (As does ping). But just now,
Firefox failed to resolve, but Konqeror is still fine.

On Dunhurst, the internet is simply unreachable. Even pinging an external IP
does not get a result.

All three computers can ping the router and each other. Tux and Dozy can ping
anything I have tried, both by address and by IP. Dunhurst can ping only the
internal network, but can ping all three nodes (?vocab?), including the
router. (Dunhurst has just failed to ping the router. :-( )

The "router" is single port and all three computers are connected to it via a
three port Home Plug. I have changed the Cat5 cables around in the plug, but
it made no difference.

Any suggestions very much welcomed.

It is possible that the router is faulty (other symptoms), but I do not see
how it could produce this particular mix. :-( Since I had already decided
that the router was faulty, that is a possible explanation.

The home hub network has always before worked perfectly and was working
immediately before I connected this new "router" up. (The internal network
worked fine still on the old "router". But it could not reach the Internet.)

**If this _could_ all be due to a faulty router, I would be grateful to be
told that too. It will give me more to go on if I have to send it back.**

TIA
Lisi