IP address from router used as access point?

I have a couple of Belkin wireless routers, one (g) connected to the cable
modem and working fine; the second one (b) was extra, so I thought maybe I
could set it as an access point and extend the range to some far points of
my house.

I set the b router (in the router setup) to be used as an access point, gave
it an assigned IP address, and plugged it into a network switch using the
WAN port (different channel and SSID than the other one)

It showed up fine in the list of available networks, but after I told the
laptop to connect and put in the WEP key, after a while it told me it was
connected but may not work right, as it couldn't get assigned an IP address.
(I assume setting the router as access point disables this (?)). It was
correct, I couldn't get the internet connection through it.

I assume the solution may be to assign a fixed IP address, but I use the
laptop to connect to many different places, and don't want to mess that up
by forcing an address that may not work in some places. Is there a way to
assign a fixed IP to only that one connection, when it's used?

Or, is that likely not the problem? Should the router-turned-access point
be assigning an address? Should the laptop be getting one through the
access point from the main router? Or is this entire experiment unfeasible
for some reason, or very complicated to set up? It seems so close, the
network is there, it connects, just can't get the IP address. Thanks for
any suggestions.

Gary