No. Unless the cable in question is SPECIFICALLY for your laptop, these X-to-HDMI cables will not work.
There is no standard for converting (other signal) into HDMI. HDMI is a digital signal using dozens of different wires, whereas AV cables only use a few wires.
Some devices can output the older AV signal through a HDMI port by only using a few of the pins on the HDMI connector. (if you have a Playstation or Xbox, this is how their AV connector works) However, this is not a standard feature of HDMI - the device, your laptop, has to be specifically designed to do this.
It IS possible to convert a HDMI signal into an older AV signal (composite, s-video or component) BUT these converters are quite expensive. It would literally be cheaper for you to just buy a new HDTV.
But all hope is not lost...
Does your TV have a DVI port? If so, you can get a HDMI/DVI cable (or just get an HDMI adapter for the DVI port.) DVI is identical to HDMI...but doesn't support audio. So you'll get the image from your laptop on the TV screen, but to get audio you'll have to run a separate cable from your laptop to your stereo. Radio Shack or your local electronics store sells a cable that has a headphone jack on one end, and the red/white audio jacks on the other end.