I strongly suspect that the answer is "none of them" and you're stuck with an old TV with no suitable connection. However if your laptop has a composite video socket - something like the yellow one you mentioned for the TV, then you could get a phono to phono lead and connect them together for video. Such sockets are unusual on newer laptops. You would also need a 3.5mm stereo jack to twin phono lead to connect from the laptop's headphone socket to the red/white audio sockets. If you did manage to get it going you might find the picture quality of DVD's barely acceptable and Facebook unuseable. The Phono to Phono connection can't give good quality.
You might want to face up to a new TV; Richer Sounds have a good selection. This one is their cheapest 32" at £199 and you can get a 5 year warrenty for £19.99.
In my experience a dedicated DVD player is more reliabile than hooking cables to a TV and although a TV has a bigger screen you'll be sitting further away, so no overall gain.