Is it possible to connect the HD Cable box to TV by component cable?

yes, and will be capable of displaying Full HD. I also recommend that you replace your existing coaxial cable inside your home With RG6 quad. it is a little pricey but it has a faster signal transfer and less signal loss than regular coaxial cable. If you want to save money this is what i did. I went to my local home depot and purchased RG6 Quad for 12 cents a foot. I bought the appropriate length. And i purchased the RG6 Quad ends to go over the ends of the cable after its stripped. This took me about 10 min's to do and saved me some cash.

no other cables are needed component cable come with 5 wires, 3 video and 2 for audio, and yes this is the best set-up for hd in your situation, and I would definately check to see if the converter has hdmi, most all hd boxes have hdmi outs, no need to but any expensive cables, just go to ebay and buy cheap ones the human eye will not be able to tell the diff between ans 100.00 cable or a 15.00 cable, you really need hdmi to clean up the other channels

Go with component cables....I would double check and see if they have a HDMI box? I can't imagine they are offering HD packages w/o boxes that come with HDMI. If not, go with component.