First, if your computer has an
HDMI connector, just connect that to the TV. Depending on the hardware in the computer, you might also get audio over that cable, or you may not.
if your computer's graphics card has a DVI
connector, you can get a
converter cable to connect it to the HDMI port of the TV. You probably won't get audio this way, though.
If you don't have HDMI audio, you might be able to run an
audio cable from the computer to the TV.
Next comes the problems with subs. As Stealthtank mentioned, there are two kinds of subs. "Hard" subs are encoded directly into the video. Most karaoke are subbed this way. "Soft" subs are decoded along with the audio and video streams and displayed by your media player. If you can't see the soft subs, your player probably doesn't have the right software to handle them.
Rather than re-encoding the video, how about just getting a player that will show everything you need. I'm going to guess you're using Windows, but if you're using Linux I'd give you the same advice. Install a copy of
smplayer; here is the
Windows version; most Linux distributions have smplayer in their repositories so just install it with your package manager.
If you're using a Mac, you might want to try this
player. If you need help, take a look at
this thread.