Would like to understand WHY changing the IP address seems to make a difference.

Question

I have had significant difficulty getting my WRT54G v5 to pass to the internet multiple pcs connected by cable and/or wireless.  Default settings seemed to work fine to log into the LAN, but only 1 connection would go to the internet.  I called Linksys tech support and they successfully got me over at least the initial hurdle so that my 2 main pcs can now function, and a 3rd seems to also get through.  I've seen in this forum a BUNCH of similar posts, including some which say that success only lasts for brief periods of time.
What changed to get mine to work???.......192.168.1.1 was changed to 192.168.2.1.  What I'd like to understand is.......why does that make a difference?
I am not a networking technical guru by any means, but am I a novice to technical discussion.  Simply changing the address to go from not working to working does not make sense to me, and I'd like it to make sense so I can support this thing without spending hours every weekend.
Linksys, can you please explain?

Answer 1

The address pool of the DHCP server are just the IP addresses which the DHCP server uses to assign them to devices which ask for an IP address via DHCP (e.g. computers which are set to obtain their IP address automatically). The DHCP server automatically supplies those devices with an IP address and assigns the correct subnet mask, gateway address, and dns servers.
This has nothing to do which IP address actually have internet access or not. After the device got its IP configuration from the DHCP server this configuration works just like any other configuration you may statically configure on some other devices.
The router connects all IP addresses inside your LAN to the internet as long as the devices use the router IP address as default gateway.
If you router has an LAN IP address 192.168.1.1 and a subnet mask 255.255.255.0 these two numbers together define that all addresses 192.168.1.* are part of the LAN. 192.168.1.0 is a special purpose address. 192.168.1.255 is the broadcast address of this LAN. Everything from 192.168.1.1-254 are normal IP addresses inside your LAN (with .1 obviously allocated by your router). Operating as gateway between the LAN and the internet the router accepts traffic from any of the LAN addresses and forwards it into the internet and receives the responses and sends them back into your LAN.
For the routing/gateway part of the router it is irrelevant where the device got its IP address from. This part does not know about the DHCP server. All that matters here is that the IP address is valid and inside the LAN subnet. If the device has a static IP address or DHCP assigned IP address does not matter.
It does not matter which IP address range the DHCP server assigns. Linksys uses 100-149 as default. Some other routers assign 2-100. Some others assign 2-254. Assign whatever you like. Orderly people split their subnet into various parts, e.g. assigning 10-19 to NAS devices with static IP, 20-29 for printers with static IP, 30-39 for VOIP phones with static IP, 50-99 for DHCP, 240-249 for other networking gear. Or in any other way.
The only important thing is not to assign a static IP address inside the DHCP server address pool. The DHCP server checks whether an IP address is used before it assigns it. If, however, the device with the static IP address inside the DHCP address pool is temporarily down, the DHCP server does not know that the IP address is used otherwise and thus may assign this address to another device. Now, once the device with the static IP address comes up again you have an IP address conflict. Therefore, never assign a static IP address inside the DHCP server address pool.