Nope; not possible.
A slingbox of any variety (classic, tuner, a/v, pro solo, or even the pro hd) is an input connection device and is not capable of distributing the signal being inputted to another straight TV. there used to be a product they sold called the sling catcher that did exactly wehat your wanting to do; however they have since discontinued that product.
You can however do the following:
In the secondary tv location you can hook up a laptop or desktop computer to the tv/monitor if your computer has some type of video output connection (s-vhs, composite, dvi or hdmi). The computer of course would also have to have some sort connection to the router. since you stated you have no ethernet jack in that room you would either have to connect wirelessly or use a slinglink (powerline adapter set) to make connection.