Of course! This setup could do up to I think 5. In order to do this you would use the gpu hdmi output and plug that into the tv and you could get a $2 dvi to vga converter or you could use a display port to vga cable. Then you will go into your desktop and right click anywhere. At the bottom of the options you will see screen resolution, click that. You will see a popup window. You will want to set the options to extend the displays and you will want to set the sony tv as your primary display. This should be good to go and it will cost you a MAXIMUM of $10-$15 if you don't have any of these pieces laying around which I would highly doubt.
You could easily run both monitors off of the GTX760; HDMI to HDMI on your 40" TV and DVI to VGA (using a DVI --> VGA adapter) on your old Sony. You'll just need to enable the Sony as a secondary, extended display. Running a game + Google Chrome at the same time shouldn't be an issue. Running two games simultaneously may be. You'll need to check your motherboard manual, but in most cases, installation of a discrete graphics card disables the on-board graphics.