Hopefully. Depends on your tv, too :D
To clarify, your external hard drive has a film saved in .mp4 (for example). It plays on your pc because your computer has a program that can recognise it and play it and the appropriate codex. If the film is played in a format the pc doesn't recognise it will not play.
Your tv doesn't have the programs or the codex so it can't play it. Your tv can be used a monitor, though, but just like your pc monitor it needs the 'brain' to read the information and display it.
Your new laptop will need to be able to display on a second monitor (the tv screen) and the tv and laptop must be able to communicate to send and receive the information and display it properly.