I have a desktop which is running but it says "No Signal" on the screen when I turn it on. It isn't the graphics card because it is integrated onto the motherboard and it isn't the screen because I use my TV screen. Can anybody suggest any possible faults that could cause this?

Just because the graphics card is integrated onto the MOBO doesn't mean it can't go bad.

Have you used this desktop on there before? Sometimes you have to manually add another viewing device or hit a hotkey to switch video to it!

As far as hardware goes,
The three things to check are:
1. The cable
2. The monitor
3. The graphics card

Do you have a spare graphics card or one you can temporarily test? Cable?

Since you use te TV and I am assuming your TV still works fine. I would guess it's either the chord or graphics card or a hotkey/setting.