The usual approach to this is to do the following.
Make sure both routers are using the same subnet. Since you say your Thompson integrated router & DSL modem must use the local IP address 10.0.0.139 it appears you must set up the WRT54G to use the 10.0.0.0 network with the same subnet mask 255.255.255.0 used by the Thompson router.
As you already know, only one router can be set as the DHCP server. It is also important that your settings for DHCP do NOT overlap/conflict with any of the fixed/static addresses on your local LAN. So pick an IP for the WRT54G which is not in your DHCP range. (You did not mention what range of IP addresses your DHCP currently uses).
Make sure you connect the two routers via an ethernet cable in one of the local LAN ports of the WRT54G. Do not use the WLAN port on the WRT54G. (This is the easiest way to avoid using NAT on the WRT54G IMO).
Make sure that the default route on whichever router you decide to use for DHCP is set to the local LAN address of your router that connects to the Internet. In other words, the default route would always be 10.0.0.139 since you said this address is "fixed" for that router. The setting for the Default Route used by the systems on your network is what determines which router they will use to access the Internet.
Don't forget to turn off the WLAN/radio in the Thompson router. If both routers are trying to use Wi-Fi I expect they would interfere with each other.
FWIW, this article may also be of some help. How To Convert a Wireless Router into an Access Point
I would also suggest you use the OpenDNS name servers since they are and free and in my opinion are a little more robust. They also provide some (very) basic filtering of malware sites. But that's probably something you'd only want to fiddle with after getting everything else to work.
Response To Comments
It appears that the modem sees the WRT54G because it is listed under "detected devices", but I find it very odd that it reports the device to use the IP 10.163.55.254! I have no idea where this address comes from, and there's no response if I ping it, nor if I point a browser there.
The IP 10.163.55.254 is used as the example in the article I provided a link to. It appears you followed the instructions in that article literally instead of using them as an example intended to be modified to fit the requirements of your situation.
In that article, the author points out that his LAN router's DHCP server range is 10.168.3.100 to 10.168.3.249. This is completely different from your situation. According to your comments, your DHCP range is 10.0.0.1 through 10.0.0.254. If you cannot change this by modifying the settings for the Thompson router's DHCP, then using an IP which is unlikely to ever be assigned by DHCP such as 10.0.0.250 is what I would try.
Not sure what you mean by "default route".
There are three basic configuration values for each system in an IPv4 network.
- A unique IP address. The IP address is used to identify the system or device on the network.
- The subnet mask to use. The subnet mask is used by the system or device to decide whether a destination IP address is on your local LAN or "remote" (i.e. somewhere else in the Internet).
- A default route. This is simply the IP address of the device to which a data packet is sent when the destination IP of the packet is not on your local LAN.
Every PC on your LAN must have these three configuration settings. And in order to successfully communicate with another device on your local LAN or on the Internet, the settings must be consistent with the settings of the other devices on your LAN.
Let's assume your laptop tries to send an IP packet to the address 10.0.0.250. The first thing done is the subnet mask in the laptops IP settings is applied to both the laptop's IP address and the destination IP.
If the subnet mask is 255.255.255.0 then the first 3 numbers of the source & destination IP addresses (i.e. 10.0.0) are compared. If they are identical, then the destination is on the local LAN and the packet is sent directly on your ethernet.
But if the source & destination IP are different, then the packet is instead sent to the IP address of the "default route" configuration setting. The device at that IP is then supposed to figure out where to send the packet next so that it eventually reaches its ultimate destination.
What is important here is that these three settings are (part of) what DHCP assigns to your laptop and other computers. If your laptop uses Windows one way you can display the values assigned to your laptop is by issuing the command ipconfig /all in a command prompt window. The value for default route should always be the address of your Thompson router since that router is the only device on your system which is connected to the Internet.
I am pretty sure you will need to always use the DHCP server on the Thompson. In order to use DHCP on the WRT54G you would also need to be able to specify the "default route" which DHCP would instruct your PCs to use. I don't think this can be done.
The DHCP in the home routers I am familiar with usually provide their own local LAN IP address as the default route. When there is only one router and it is the only way to reach the Internet this assumption works. But when you are adding a second router as an alternate Wireless Access Point, the default route still has to be the local LAN IP of the router which is connected to the Internet which would be your Thompson.
Hope this helps some.
2'nd Response To Comments
About the IP 10.163.55.254: This address was listed in my modem's device list even before I began changing anything; that's what confuses me. I am very sure that I did not enter that IP during my configuration attempts.
Well, in that case I'm totally clueless. This whole business about not being able to configure the Thompson's DHCP range and its IP address being "hardwired" to 10.0.0.138 makes no kind of sense to me. For one thing, the Thompson's IP address should also not be in the DHCP range. Sure it's unlikely that IP would ever be assigned, but still ... it's just sloppy.
Oh, well. Perhaps you'll have some luck with the suggestion in the other answer to somehow convert the Thompson to act just as a DSL modem.
Alternately I suggest contacting your service provider and asking if they can supply you with a DSL modem without an integrated router. Or if they can't do that, perhaps you can exchange the current router for a "newer" one ... or at least one with newer firmware ... which might actually let you configure it.
One other thing I've wondered about is if you've ever tried resetting the Thompson to the factory defaults. That's the sort of thing I would try just to see if anything in the router's configuration changed. To do this try pushing the recessed Reset button on the back of the Thompson router between the power socket and the LAN ports with a pen or an unfolded paperclip. Push it until the Power LED lights red or around 10 seconds.
I just find it hard to believe that the current configuration is the "factory default". For one thing, here is what the documentation I found which I think is for this router says to do to navigate to the browser configuration interface:
If the default local LAN IP for the router is supposed to be 192.168.1.254 then how did it get set to 10.0.0.138?? And what else has been "mucked with".
FWIW, here is a link to the where Google found some documentation for a THOMSON TG585v7. I'm not sure if it pertains to the router you have though.
