Yes, you probably can do it quite cheaply. If you are using a graphics card it should have some sort of video output. But it bit more info is needed, what sort of graphics card do you have, someone should be able to tell you what output facilities its got. Also have a look at the back of the telly box and have a look at what connections you've got there, you'll probably see a SCART socket which looks like a large multi-pole socket and maybe some others as well.
You may find you only need a lead which will cost between £4 and £7.