I have a modem router (TP-Link TD-W8961ND) connected to the internet and working fine. It is broadcasting a wireless network and that too works fine.
I have a second modem router (Siemens SL2-141) functioning as an extender. It is wired to the first router and broadcasting a wireless network with the same SSID, same security, but on a different channel. DHCP and UPnP are disabled on the second router.
My iPad, iPhone, and Win7-based ThinkPad are all able to move between the two networks with no problems.
We also have a WinXP SP2 Netbook. When in proximity to Router1, this machine accesses the LAN and Internet with no problems. As soon as it gets closer to Router2, it picks up the signal and shows an "Excellent"/"Strong" connection but it can no longer see the internet. It can see Router2's config page and the other machines on the network but it cannot get past the router to the internet.