1.
BEFSR41. This model number is not "wireless", although the "BEFSR41W" is.
2.
Documentation. So far I've only been able to find the Quick Installation guide for BEFSR41 version 2 from its
support page. (Be sure to select "Version 2.0" on that page).
3.
APIPA Address. The IP address you posted earlier is an Automatic Private IP Addressing (APIPA) address. When your NIC interface is configured to get an IP Address automatically (through the DHCP protocol), and a DHCP server cannot be found or does not respond; Windows will arbitrarily assign an address within the APIPA range with a Subnet Mask of "255.255.0.0".
This means either you are not logically connected with the Linksys router or its DHCP server function is "disabled".
4.
Objective. Do you just want to use the BEFSR41 as a "switch" to network four devices together or do you also want access to the "router" functionality?
5.
Reset Factory Defaults. The Quick Installation pamphlet has instructions to perform a hardware "reset" back to factory defaults. This resets the configuration web page address of router to "192.168.1.1" as well as resetting the "user" and "password" values.
I'd think twice before doing this; issues being is it yours to "modify" (ownership) and does it use standard Linksys firmware? Although if I were to write new firmware, I would either disable the "reset" button or program it to be compatible with new image. So maybe that's a non-issue...