With respect, I don't believe Kees to be correct here, but I'll get to that later.
Back to the sub...How do you connect the sub to your laptop? Many of my friends have "2.1" computer speakers and the sub connects to the PC and the speakers connect to sub. Can you do this? Look for two "headphones"-sized jacks on your sub. You'll have to figure out which one is which. Plug the speakers into the "output", and then connect the sub to the TV via the "input" on the sub. I'd also suggest turning down the volume on the sub/speakers first before connecting anything, even if the "volume" is on one of the speakers itself (the sub has it's own volume, although it's downstream of the speaker/master volume).
Re: the headphones jack, it's completely analog, and so it has no idea what's being plugged into it, be it speakers, headphones, a dishwasher, whatever you can get to fit into that hole. Additionally, I've never met a TV that has a high-pass crossover applied to the headphones jack. Also, most "computer speaker" systems come with a powered sub; in fact I can think over very few passive subwoofers available, and none of them are sold as "computer speakers' (they're hundreds of dollars). I bet that it already has an amp, and if you can connect the sub to the tv (anyway you can: 3.5mm to 3.5mm, 3.5mm to RCA, whatever) it's gonna make sound.
Let me know.