The setup should usually (by not always) be like this.
modem > Router > PC1
or
modem/Router > PC1
Modem is setup and admin by your ISP which should provide you with all IPs
Router is setup by you and usually with the first IP in your network. Eg 192.168.0.1. You also setup your wifi network fromt he router with SSID and passphrase.
PC1 connecting to Router port should be only auto detect (all settings). And should have the next IP avialble which is 192.168.0.2 if it's not already taken by the another device on your network. Try connecting to the net and see if it all works.
PC2 picks up wifi network and connects. IPs should be all the same exact it's the next IP number available. Eg 192.168.0.3.
If both can internet access and give valide IPs you are done.
Try pining PC1 to PC2 and vice versa. Change to difference Port for PC1 if need be.
Uhhhhh Ummm Uhhhh Doooh... the Gateway, DHCP, and DNS are always the IP of the router on a SOHO network (Unless DNS is manually configured)! I am totally amazed at why are you amazed by this???
damit3:
Lets look at this historically... when did the issue start? Im willing to bet your I realize that you are trying to network, but... Did Internet work fine until you added a router and 2nd PC??? Does either PC connect to Internet?
My Computer
At a glance
Windows 7 Ultimate 64 bit Steve Ballmer Signa...Intel Core 2 Quad - Q9550 - 2.83GHz stock - O...4GB DDR2 800MHz (PC6400) OCZ ReaperNvidia GE Force 8800 GTS
Computer Manufacturer/Model Number
Homebrew PC - "Alpha_Dawg"
OS
Windows 7 Ultimate 64 bit Steve Ballmer Signature Edition