It sounds like my suspicions were correct. HDMI is a digital interface. Coax, composite, component, and S-Video are all analog interfaces and your TV is not doing the conversion from digital to analog (to be honest, I'm not sure any TV does). The Headphones output of your laptop is also an analog source, so you should be able to connect the HDTV to your laptop using HDMI (for video only) and your headphones output of your laptop to your tower speaker (the speakers are powered so no need for a amplifier) using a cable like this one
This set up, while a bit messy, should work for you.