Doing a crash course in networking isn't going to be easy, so I'm going to ask you to look around. Remember, once configured in bridge, the modem's IP address doesn't mean much.
So, I'd like you to look around and don't save any settings.
Look at your modem's config page and find where they talk about Bridge. The IP address of the modem. What is it? 192.168.1.1, I think. The Subnet mask should be 255.255.255.0 in most cases.
See where it talks about assigning addresses automatically (DHCP) (what range is listed?) What is the fixed Ip address range.
It should also talk about NAT which they might call sharing an IP address or a group of IP addresses.
Don't confuse the DHCP address it get's for itself. In other words, in the configuration for the ISP, it will talk about PPPOE, Username, Password. The public IP address should be assigned by the ISP and not fixed.
Learn how to back-up the settings.
Now look at the wireless router and find the same sort of settings. PPPOE; IP address; range of DHCP; range of fixed addresses. NAT. There should not be any entries for PPPOE at this point.
What also happens in the way I think your set up is you will have difficulty seeing wired and wireless clients.
To give you a couple of hints:
Your modem should have a fixed IP address and the default is probably OK because of troubleshooting.
You need to be able to connect wired to this modem for configuration purposes and I think you need a crossover cable to do so, unless your laptop is an auto-midx.
Say your modem is 192.168.1.1 and you have either midx ports or an x-over cable. You need to set your "WIRED" connection address on your laptop to something like 192.168.1.200, a SM of 255.255.255.0 (probably 0.0.0.0 will work too); Basically something on the network of the router. Who cares about name servers and default gateway.
This is not a link between your laptop and your modem. If the modem is bridge only stats, and a few other things will work. You should be able to type
http://192.168.1.1 and access your modem's configuration page.
That's all I care about. Can you do that?
Eventually the wireless router will also be given a fixed IP address like 192.168.1.2, SM of 255.255.255.0 and you need to access it the same way. It could have the same address. Normally this is a No No.
In here, DHCP will spit out addresses from 192.168.1.3 to say 192.168.1.20 and sharing IP addresses (NAT) should be enabled. I like using a long lease times, like years.
Network printers should be given fixed IP addreses.
Eventually connection must be changed to PPOE with the same username, password that the modem is using. The uplink port of this router will eventually be connected to the modem in bridge mode with NAT and DHCP disabled in the modem.
Once this happens, you can connect via the non-uplink ports and access the linksys page. The modem will be OFF LIMITS unless you connct to it directly.
When everything is working, you can either have everyone connect via DHCP or give them fixed addresses.
Since windows make it difficult to have settings, DHCP for wireless connections seems to be best all around because it works at hot spots too. With high lease times you'll typically get the same address assigned when at home.
What happens when your all done is that the modem "bridges" the telco connection to ethernet with no smarts and the linksys router takes on all the functions of firewall, port forwarding, DHCP, NAT etc. The wired and wireless connections will be in the same IP address range.
I don't know what's going on in your set up, but having two DHCP servers and two devices doing NAT, you will have problems.
SO, look around. Don't save anything. Figure out how to backup settings.
I know what I said is confusing and doesn't make sense.