You can use a S-video cable. If the TV accepts s-video then you are done.
S-video cable:
If it doesn't you would probably need a s-video to scart converter plug kindoff thing.
Like this:
Then if it works you are done. If not (and by not I mean that the above plug could cause a black and white image on your tv) you should curse for a short while and buy an s-video to composit plug which you can then plug in between your s-video cable and your scart plug.
That should look like this:
There is also an alternative way of getting a signal to your TV which is using your VGA output. That would most likely be more expensive. If you want to know about that as well then ask for it and I'll try to explain that as well.
Edit: For as far as I could find out your laptop only has a s-video out and a VGA out. No TV out that I could find.
Edit II: I just noticed I linked the wrong image for the s-video to composit converter. The s-video side should be female instead of male and the composit side should be male instead of female.
Also, I don't know how old your TV is and whether it accepts scart or composit only. If it only accepts composit you won't have to buy the s-video to scart plug obviously.
My advice would be to go to a electronic part shop and talk to someone there. They will be able to tell you what you need just fine.
Edit III (this is really the last edit): I don't know how broken the LCD screen is, but you will need to turn on the external screen somehow so that might be a bit hard. Maybe there is a hotkey for it though. (fn+F5 most of the times)