This is relatively easy. (for computers network, I don't know for routers, but it could help you).
First you have to forgot that this is your computer which has an IP (like 192.168.0.1). It's not the computer but the network card which actually has an IP assigned to it.
What you'll need to do is set all the IP manually.
I'll detail the way to connect 1 PC to both 1 computer and 1 router.
The connected computer will gain internet access through NAT.
I concider the Router you use to access internet to have IP 192.168.0.1
Consider your computer 2 (the one with the internet access) with 2 network adapters : an Ethernet card and a WiFi card.
Each adapters must have their own network, they can't share it.
Let's call your Wifi network the "network 0", and the LAN the "network 1".
[PC1 | ethernet card ] ---- LAN ------ [ ethernet card | PC2 | wifi card ] ------ Wifi ----- [router] ---- Internet
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Each network adapter will have a number assigned on his own network.
[PC1 | ethernet card ] ---- LAN ------ [ ethernet card | PC2 | wifi card ] ------ Wifi ----- [router] ---- Internet
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You made your visual network repartition and assigned number to both the network and the adapter on the network:
PC 1 ethernet has <!--coloro:#0000FF--><span style="color:#0000FF"><!--/coloro-->IP 2<!--colorc--></span><!--/colorc--> on <!--coloro:#FF0000--><span style="color:#FF0000"><!--/coloro-->network 1<!--colorc--></span><!--/colorc-->
PC 2 ethernet has <!--coloro:#0000FF--><span style="color:#0000FF"><!--/coloro-->IP 1<!--colorc--></span><!--/colorc--> on <!--coloro:#FF0000--><span style="color:#FF0000"><!--/coloro-->network 1<!--colorc--></span><!--/colorc-->
PC 2 Wifi has <!--coloro:#0000FF--><span style="color:#0000FF"><!--/coloro-->IP 2<!--colorc--></span><!--/colorc--> on <!--coloro:#FF0000--><span style="color:#FF0000"><!--/coloro-->network 0<!--colorc--></span><!--/colorc-->
Router (wifi) has <!--coloro:#0000FF--><span style="color:#0000FF"><!--/coloro-->IP 1<!--colorc--></span><!--/colorc--> on <!--coloro:#FF0000--><span style="color:#FF0000"><!--/coloro-->network 0<!--colorc--></span><!--/colorc-->
Now, you need to set the IP on your computer :
• PC1:
Start > settings > network adapter
Right-click on the LAN adapter icon > preferences > in the list double-click on TCP/IP
Manually set :
IP : 192.168.<!--coloro:#FF0000--><span style="color:#FF0000"><!--/coloro-->1<!--colorc--></span><!--/colorc-->.<!--coloro:#0000FF--><span style="color:#0000FF"><!--/coloro-->2<!--colorc--></span><!--/colorc--> <--- IP <!--coloro:#0000FF--><span style="color:#0000FF"><!--/coloro-->2<!--colorc--></span><!--/colorc--> of network <!--coloro:#FF0000--><span style="color:#FF0000"><!--/coloro-->1<!--colorc--></span><!--/colorc-->
sub-Mask : 255.255.255.0 (just type that, if not automatically filled). It's purpose is to define the maximum IP per network. you don't need more than 256 different IP, so type that value.
gateway : 192.168.<!--coloro:#FF0000--><span style="color:#FF0000"><!--/coloro-->1<!--colorc--></span><!--/colorc-->.<!--coloro:#0000FF--><span style="color:#0000FF"><!--/coloro-->1<!--colorc--></span><!--/colorc--> <--- the gateway is the computer allowing access to internet, so you are telling to this PC to use PC2 as the gateway. (card <!--coloro:#FF0000--><span style="color:#FF0000"><!--/coloro-->1<!--colorc--></span><!--/colorc-->.<!--coloro:#0000FF--><span style="color:#0000FF"><!--/coloro-->1<!--colorc--></span><!--/colorc--> is on PC2)
DNS : 8.8.8.8 and 8.8.4.4 (this is the Google's DNS)
• PC2:
Start > settings > network adapter
Right-click on the LAN adapter icon > preferences > in the list double-click on TCP/IP
Manually set :
IP : 192.168.<!--coloro:#FF0000--><span style="color:#FF0000"><!--/coloro-->1<!--colorc--></span><!--/colorc-->.<!--coloro:#0000FF--><span style="color:#0000FF"><!--/coloro-->1<!--colorc--></span><!--/colorc--> <--- IP <!--coloro:#0000FF--><span style="color:#0000FF"><!--/coloro-->1<!--colorc--></span><!--/colorc--> of network <!--coloro:#FF0000--><span style="color:#FF0000"><!--/coloro-->1<!--colorc--></span><!--/colorc-->
sub-Mask : 255.255.255.0
gateway : empty <--- the PC1 doesn't need to access internet through PC2
DNS : empty, same as above, no internet access needed through this connection.
• PC2:
Start > settings > network adapter
Right-click on the WiFi adapter icon > preferences > in the list double-click on TCP/IP
Manually set :
IP : 192.168.<!--coloro:#FF0000--><span style="color:#FF0000"><!--/coloro-->0<!--colorc--></span><!--/colorc-->.<!--coloro:#0000FF--><span style="color:#0000FF"><!--/coloro-->2<!--colorc--></span><!--/colorc--> <--- IP <!--coloro:#0000FF--><span style="color:#0000FF"><!--/coloro-->2<!--colorc--></span><!--/colorc--> of network <!--coloro:#FF0000--><span style="color:#FF0000"><!--/coloro-->0<!--colorc--></span><!--/colorc-->
sub-Mask : 255.255.255.0
gateway : 192.168.<!--coloro:#FF0000--><span style="color:#FF0000"><!--/coloro-->0<!--colorc--></span><!--/colorc-->.<!--coloro:#0000FF--><span style="color:#0000FF"><!--/coloro-->1<!--colorc--></span><!--/colorc--> <--- the gateway is the router's IP allowing access to internet, so you are telling to this PC to use Router as the gateway.
DNS : 8.8.8.8 and 8.8.4.4 (this is the Google's DNS)
You need to tell the WiFi network card to share internet with the other network cards of the PC1 :
• PC2:
Start > settings > network adapter
Right-click on the WiFi adapter icon > preferences > Advanced tab > select the Ethernet network in the drop down list, and check "Allow other users from this network card to access internet from this computer"
(you may need to be disconnected to do the ICS - Internet Connection Sharing)
Done <img src="style_emoticons/<#EMO_DIR#>/smile.gif" style="vertical-align:middle" emoid="
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• Router:
if you need to change the router's IP, connect to the router through your internet browser
<a href="http://192.168.0.1" target="_blank">http://192.168.0.1</a>, and go to it's IP setting.
Now, what I understand, is that you want to use 2 internet routers, both are connected to a different internet provider/account ?
I don't know if this is possible to share 2 internet connexion at the same time (for example to download quicker), but it should work.
Back on Windows 95, it was possible to use 2 modem 56k to make the download faster.
If you understood how network and network adapter are set, you should be able to create your 2 different network (1 for each router).
But it's only IF your 2 router don't share the same fixed IP.
Sometime, routers are set to "192.168.1.1" and can't be changed.
Other routers let you set the router's IP manually, so you can just choose a different "network" number for both routers.