Like this then...?
ASDL connection ( RJ11 from ISP) ------> BiPac 5200 ------ethernet cable --------> Linksys WAN port ----> wired and wireless network devices.
The BiPac 5200 is a modem/router and its settings (default or otherwise) being duplicated by the Linksys router.
Most likely your setup is misconfigured and appears to work okay (after reset) until something like a duplicate IP address is assigned by either the Bipac or Linksys.
Here is a link to the Bipac 5200 User Manual:
http://au.billion.com/downloads/usermanual/adsl/BIPAC-5200-Manual.pdf
The installation procedure starts on Page 18. However, you should read all of the manual beforehand and make some notes where you have questions or concerns.
Reset both the BiPac and the Linksys and work through the full installation setup very carefully.
Probably best to double check that the physical connectivity matches what is required for both the BiPac and the Linksys.
Secondly, the BiPac's DHCP function should be disabled. Let the Linksys router handle DHCP IP addressing. If you connect your computer directly to the Bipac you can gain browser access to the configuration pages per the user's manual - IP is 192.168.1.254 per the default settings on pages 22 and 23. Let all of the diagnostic tests run as well. Likewise for the Linksys. Both devices are wireless capable so you should disable that function - do that on the BiPac as well.
You can get to the Linksys's admin pages by using 192.168.1.1
Unfortunately the problem is a bit too broad to cover all of the possibilities in a couple of postings.
However, if you carefully work through the setup, installation, and configuration process you will most likely either get it all to work or find a specific problem that can be posted and subsequently addressed. Follow the diagrams applicable to your devices. Take your time, double check everything and keep notes.