Thanks for the information. Your observation from the Westell modem/router is consistent with what your ISP told you: your modem is assigned an IP address by a DHCP server at your ISP.
Your two pieces of equipment actually have multiple parts. Both of them have modems, which is the interface between you and your ISP. Both of them have routers. A router is necessary between two networks; in your case, these are the Internet on one side and your Local Area Network (LAN) on the other side. The Motorola unit also incorporates a wireless access point.
You only need one of each part: one modem, one router, and one wireless access point.
Normally, you should be able to use the Motorola unit and dispense with the Westell unit. However, the Motorola unit's modem seems to have a problem connecting to your ISP. According to the User Guide I found for it, this Motorola unit doesn't seem to be able to connect to the type of system used by your ISP.
So you can use parts of both devices: the modem and router from the Westell unit and the wireless access point from the Motorola unit.
I'm going to assume that this is the User Guide for your Motorola device --> http://www.arrisi.com/modems/datasheet/2247-n8/2247_user_manual.pdf
Connect an Ethernet cable between your computer and one of the 4 yellow Ethernet ports on the Motorola unit. Open a web browser and type http://192.168.1.254 into the address bar and press Enter (see User Guide page 13). You may or may not assign a password for the configuration utility (you should eventually do this) as described in step 4. Skip steps 5-7.
Click the "Configure" link (page 16) and then click "DHCP server." UNcheck the box for "DHCP Server Enable" and then click "Apply changes." You want to disable the DHCP server in the Motorola unit because you will be using the DHCP server in the Westell unit.
If you haven't already done so, go back to the Configure menu and click "Wireless" and configure the "Wireless Base Settings" (p. 21) You want wireless to be Enabled, you want the "Standard" to be compatible with your laptop and other wireless devices (B/G/N is the most flexible; use G-only or N-only if you know that all of your wireless devices use the same wireless standard). I recommend UNchecking Wireless Protected Setup. "Channel" should be 1, 6, or 11 (you may or may not need to change the channel; generally, this is only necessary if you live in a neighborhood where there are many nearby wireless networks, like an apartment building).
In the "Wireless security" section (p. 23) choose WPA2 if all of your wireless devices support this standard; otherwise use WPA. Do not use WEP or nothing. Do not "Hide SSID" or "Block Wireless Bridging." If you want, enter a new SSID name (p. 24); if you do this, don't use your name or address as part of the SSID name.
Make sure that you click "Apply changes" any time you make a configuration change.
At this point, you can exit the Motorola's configuration utility.
Disconnect any phone cable connected to the Motorola's DSL input.
Connect the phone cable between your wall outlet and the DSL input on the Westell unit.
Connect an Ethernet cable between the "Data" port on the back of the Westell unit and one of the yellow Ethernet ports on the Motorola unit.
At this point you should be able to access the Internet using (a) any device connected by wifi to the Motorola unit or (b) any device connected to one of the 3 yellow Ethernet ports on the Motorola unit that is not being used to connect to the Westell unit.
Final words:
If you have created a password to access either unit's configuration utility (and you should), write it down on a piece of paper and tape the paper to the unit.
The IP address you need to use in order to access the configuration unit of the Westell unit is 192.168.1.1. Write this down on the same piece of paper as the Westell's password and tape it to the Westell unit.
The IP address you need to use in order to access the configuration utility of the Motorola unit is 192.168.1.254. Write this down on the same piece of paper as the Motorola's password and tape it to the Motorola unit.
The DHCP server in the Westell unit defaults to assigning local IP addresses between 192.168.1.15 and 192.168.1.47. This should be more than enough. You can check the local IP address of any Windows computer by opening a Command Prompt window and typing
ipconfig /all {Press Enter}
This will show you the IP addresses assigned to all network adapters (wired and wireless). You need only be concerned with IPv4 addresses (not IPv6).
Note that if you open a web browser and go to a site such as http://www.whatismyip.com/ you will be able to see the public IP address assigned to your Westell modem by your ISP's DHCP server. In this instance, "public" means that everyone on the Internet can see this address. However, the Westell router "hides" the local IP addresses of your devices so these are not visible on the Internet.