What IP ranges are you using on each router? Is DHCP disabled on one? Do you understand routing?
Here is the problem, I have to guess a little but probably correct.
The linksys routers all use 192.168.1.1 as the default IP address (on the LAN) Guess what, so does the ASUS! I had to look the manual up but I did find it and it says "
To set IP address manually, you need to know the default settings of the ASUS Wireless Router:
• IP address 192.168.1.1
• Subnet Mask 255.255.255.0"
You can not have two routers on one network using the same IP ranges! THEY WON"T WORK!
I don't know why or what your purpose is of needing two routers but one of them will either have to be assigned a fixed address and have its DHCP turned off, or the IP ranges used as the default range will have to be changed! That is just basic networks and basic routing.
If you have it connected as you show, change the IP ranges on the ASUS to say 192.168.10.x or 192.168.2.x anything except 192.168.1.x which is where it sits by default. Then both routers will work and you will have TWO Separate networks. One off the linksys using 192.168.1.x and one on the ASUS using 192.168.10.x (or whatever). The STATIC IP that you should then set on the WAN/INTERNET side of the Asus would be like 192.168.1.10 subnet 255.255.255.0 Gateway of 192.168.1.1 and on the Linksys put that IP 192.168.1.10 into the DMZ of the linksys! Now they both will work, both will access the internet, both are "isolated" networks.
(WAN=INTERNET or Wide Area Network WLAN= Wireless LAN)
The best advice I can give you is don't use two routers unless you absolutely have to for some reason! If you do use two, they can not both be on the same IP or IP range.
If you just want to use the ASUS as a wireless access point, Login to the interface, turn off the DHCP server option, connect the wire from the Linksys (LAN port) to any of the ASUS LAN ports - don't use the internet/wide area network /WAN port. The Asus will then become a simple AP for extension of range.
Edit - If you are asking to ISOLATE the wireless from the wired network with wireless running on both units and the Asus being used as a second extension of the Linksys.
You need to put DD-WRT, or Open-WRT firmware on the units! The firmware on either of them does not have Wireless isolation. DD-WRT can do that on the Linksys but your Asus unit can not load either of these firmwares.
For the Wireless to be isolated the software in the router has to support isolation. There are routers that do support the function, but these two as they sit do not. Check into DD-WRT or Open-WRT for the Linksys, Then you can isolate the wireless on the Linksys. Other wise setup the linksys WITHOUT wifi and the Asus with WIFI on a separate network. Then the ASUS will have "isolated" wireless on a separate network.