You might be able to do what you propose, I've certainly done it with a standard wireless router in place of your 2nd modem/router. However, you would have to be able to log into the 2nd, currently unused modem/router (using a web browser) as an administrator and configure it, if possible. I would hope that the fact that it has a modem in it will not interfere with essentially turning it into a switch, or a wireless access point.
Connect the 2nd modem/router to the first one with the LAN ports, one LAN port from first modem/router to a LAN port on the 2nd modem/router.
So log into the 2nd modem/router and turn OFF DHCP, so it isn't handing out addresses (your first modem/router will handle those duties).
Then assign it a static NAT address in the same range that your first modem/router is using. For instance, if your router/modem is set to 192.168.1.1, then you would assign the static IP address to the 2nd modem/router as 192.168.1.2 (this assumes that the first modem/router is starting its DHCP range of addresses somewhat higher, such as 192.168.1.100-200); if not set it to something like that).
At this point the 2nd modem/router will be sitting there with an address of 192.168.1.2. Make sure to tell it that it has a static IP address (most such devices are set to grab one handed out by the local headquarters of your ISP, the other end of the ADSL line).
When you're done you can test this by connecting an Ethernet cable from your PC to one of the LAN ports on the 2nd modem/router. You should automatically get an IP addresses handed out by the first modem/router, through the 2nd, and on to your Ethernet port.
If this works, then you can log onto the 2nd modem/router and go into the wireless settings and set up whatever security and other details you want to.
But all this hinges on your being able to log onto the 2nd modem/router, and that it will function like a router in the absence of a direct Internet connection (I think it should).
EDIT: I would connect to the 2nd modem/router with an Ethernet cable from your PC to one of its LAN ports and configure it BEFORE you connect it to the first modem/router. That instruction was placed in the wrong part of the upper instructions. Wait until you have it configured before you connect it.