Need advice on making a repeater to share broadband

My neighbor and I would like to share a DSL internet connection. He has a Linksys BEFW11S4 V4 wireless router. I can get good reception only when I am by a window that faces him. I'd like to be able to get wireless throughout my home. I'd like to be able to setup a repeater as cheaply as possible. I have a SMC 2655W Access Point and a D-Link DI-524 wireless router. My idea is to use my SMC AP(in the window) to connect wirelessly to his Linksys router and then run a Cat5 Ethernet cable from my SMC AP to my D-Link wireless router(centrally located in my house) which will broadcast wireless throughout my house. The Atmel utility will allow me to configure the SMC

2655W in three modes of operation. It can be an access point, an access point client or a bridge. I figured I'd configure the SMC AP as an AP client. I can then have the SMC AP associate and connect with his Linksys. However, for some reason my SMC 2655W AP will not work as an access point client with his Linksys BEFW11S4. Perhaps they are not compatible? They are both 802.11b and we've turned encryption off right for now. If I use a cross wired Ethernet cable and connect my PC directly to the SMC AP while it's associated with his Linksys in AP Client mode, my PC will obtain an IP address from the DHCP server in his Linksys. But, I can't ping his Linksys router or his computer and needless to say, I can't surf the web. However, I can get the SMC AP to work fine as an AP client with other brands of wireless routers, including my D-Link router. So, I know the SMC AP will work correctly as an AP client. Does anyone know why the SMC 2655 will not work as an AP client with a Linksys BEFW11S4?

As I mentioned, the Atmel utility will also let me put the SMC AP into bridge mode. I can't use bridge mode because bridge mode requires two APs, both running in bridge mode and I only have one SMC AP. I could buy another AP that will run in bridge mode, but before I purchase more hardware, I'd like to get some suggestions. Is there a way to use the hardware we already have? If not, what about this Motorola WE800G bridge:

? I saw this for just $35! They call it a bridge, but it appears to me to work as an access point client because it does not require a connection to another AP in bridge mode. Is there any difference in the function of the Motorola bridge and the SMC when it's in AP client mode? Does anyone know if there are compatibility problems with the Motorola WE800 when connected wirelessly to the BEFW11S4 V4? Any help would be appreciated.

Thank you, Steve Smith