There is some good advice in the answers above.
And I'd personally go for the "get rid of your linksys router and use the d-link router instead since it can do exactly what you want.
BUT
Another option is to use the DI-524 from D-Link as a wireless access point only and "disable" the router portion of it.
To do this you simply turn off the DHCP feature within the DI-524 and not use the WAN port for anything. Just plug in your Ethernet cable to a LAN port on the original router and in the LAN port of the DI-524.
The trick to this is that the DI-524 and the BEFSX41 need to be on the same subnet (aka network). By default linksys routers are 192.168.1.1 and D-Link is 192.168.0.1 So change one or the other's LAN IP address to what subnet you want to use. (subnet = 192.168.0.X or 192.168.1.X) When devices are on different subnet they can't "see" each other with out extra configuration.
So if you want step-by-step;
Login to the DI-524 and DISABLE the DHCP feature. - This will make sure the DI-524 doesn't try and hand out IP addresses and fight with the BEFSX41, since the BEFSX41 is already handing out IP addresses (DHCP enabled). [by default]
Next change LAN IP address of DI-524 to match with the same subnet of the BEFsx41. (ie. probably 192.168.1.2 - This will connect your two networks together. Remember that you will now have
access the DI-524 web interface on 192.168.1.2 (whatever you set it to).
Then if the laptop is connected wirelessly to the DI-524 and the 524 is configured like above you should be able to access the Internet. Then if Internet works, you should be able to do file sharing and print sharing.
BUT to make it all easier, just like others have said, get rid of the BEFSX41 (don't forget to write down all configurations so you can enter them into the DI-524) and just use the DI-524 to handle your internet connection, DHCP, wireless, and wired network.