connecting PC to TV - need help

Total newbie here...hope you guys can help.
I am trying to connect my HDTV to my PC as a monitor. The TV has a VGA output, and I've successfully connected to my computer through that. However, I wanted to be able to have both my original PC monitor on and the TV on at the same time, sort of an "extended desktop" deal (mainly to be able to watch movies stored on my PC through the TV, which is not next to the PC but on the other side of the room).
I am currently trying the following set-up, and it's not working:
- I connected a VGA- to - VGA-and-DVI adapter/splitter to the VGA output on my PC
- to the VGA output of the adapter/splitter, I connected my original monitor
- to the DVI output of the adapter/splitter, I connected a DVI-to-HDMI cable
- then I connected the HDMI end of the cable to the HDMI output on the TV

The monitor is on, but the TV is showing "no signal." What am I doing wrong here?

If I connect the TV to my PC through VGA, I need a separate audio connection.
Although I suppose connecting DVI-to-HDMI needs a separate audio connection as well, right?

Can I do a VGA-to-component connection from my PC to the TV, instead of VGA-to-VGA, just so I wouldn't need a separate audio cable?

So if my video card only has a VGA output, there's no way I can connect my computer to the TV via HDMI, correct?