I just bought a new internet capable Sony TV and would like to hard-wire connect (for better speed and reception) it to my Verizon DSL service so I can take advantage of the online apps. My problem is the location of my present wireless modem/router (Westell 7500) which would require me to install an ethernet cable through my walls and through my attic to make the connection. Instead I thought maybe if I purchase a wired modem/router and located it next to the TV (a telephone connection is located there) it might be my easiest solution. What I am concerned about is whether two modem can coexist in that environment at the same time, and if so; whether there are setup issue of which I need to be aware.
Two modems cannot co-exist on the same line. You can daisy chain the routers but you still need to run an Ethernet cable between them. However your speed argument doesn't hold up. The 802.11b is good for about 11mbps, and 802.11g is good for about 54mbps, either is likely to be substantially faster than your DSL internet connection. So if the TV supports wireless, speed isn't a good reason not to do so.
If your TV doesn't support wireless (Wi-Fi), you could connect it with an Ethernet Bridge.
The bridge converts the hardwired Ethernet to Wireless and back, so your TV sees a hardwired connection, that in reality is wireless.
In your application, an 802.11b or 802.11g bridge would probably work. If you plan to have anyone else on your Wi-Fi network, 802.11g is preferable. These are available on eBay (and many computer stores) at reasonable cost.
D-Link, SMC and Linksys all make such devices. There are probably other manufacturers as well.