Turn it on

Yeah, I did all that, but the TV says "no signal".

Edited:

How do I do that?

Your video drivers should have a section to manage multiple displays. How this section is called, and what the options are, depends on which card you have. Look for this section and configure the settings to extend your desktop to the secondary display (which will be your TV set) or, failing that, to clone it to the secondary display (suboptimal because in this latter case the resolution, form factor and colour depth will be the same as your primary display, while in the first case you can set them separately).
To route audio to the HDMI cable you probably will have to install the appropriate driver for your video card (in my case it comes separately from the main display driver); this in turn may require a MS patch if you are running Windows XP and haven't installed SP3.
Personally I'm using the TV set as the primary display while I'm using FS (there's an option to switch positions on the fly so that display #1 becomes #2 and vice versa, while retaining individual settings) so I can run FS at 1920x1080 (1080p, "FullHD").

You should have a button on the controller of your TV that says input. Try changing that to the appropriate input.

The TV set should be automatically recognized and picked up by the CCC as soon as you connect it.
I suspect a cable issue, or perhaps a weird compatibility issue with your TV set.
Either that, or you have improperly installed the video driver, the HDMI audio driver (and patch if needed) or CCC.
If you can, try another cable and/or a different TV.
If you are going to use a 1920x1080 resolution you will want a FullHD certified HDMI cable otherwise issues will arise.

When i plug my hdmi to one of my 5770 ati cards it works straight away please post a pic of your remote control. You should be able to keep pressing the AV button until you get the right channel for your pc. Remember to make sure it's all running.

the thing is that the TV set should appear in CCC as soon as it's plugged in, no matter the channel it's tuned to. in my case the TV shows up in CCC even if it's switched off (standby), I don't even need to turn it on.

Here is what I'd do:
1) completely uninstall the video driver, the HDMI audio driver and the Catalyst Control Center, in short all the ATI drivers and software pertaining to the video card
2) reboot in Safe Mode and run Driver Sweeper to get rid of leftovers
3) reboot in normal mode and reinstall the video driver, the HDMI audio driver and the CCC
If it still doesn't work, I'd try with a different cable and/or a different TV set (logically, this should be done before all the other steps, but since it probably is a problem to find another cable... for free... or take the PC to a friend's to try with a different TV set... if you can borrow an HDMI cable you should try that first).

Press F8 at startup, then choose safe mode from the menu.
If you come to a point that your TV set appears in CCC, then set the "extend desktop horizontally" option, select display #2 (TV) and start with a conservative resolution from the drop down menu, one which your TV can surely handle; set the refresh rate at the maximum allowed (probably 60 Hz); then work your way up to the max resolution allowed by the TV set (720p or 1080i or 1080p, worst to best, depending on the TV)