What you need is an HDMI to component converter. HDMI signals are digital and component signals are analog so no amount of simple cabling is going to resolve that issue.
Essentially, TVs of whatever incarnation are analog devices. They have to be, because our eyes are analog. We can't receive and decode digital signals, so in each modern TV there is a DAC (Digital to Analog Converter) which does the conversion.
If your TV has no digital inputs, then what you need to do is buy an HD Fury 3 device, plug it into your component inputs and this will then effectively provide two HDMI inputs on your TV. It is only doing externally what usually happens internally on a more recent TV. In fact, the HDFury is very high quality so will effectively give you a better conversion than most cheap internal DACs.
I have done exactly this on my system and since the HDFury is fully HDCP compliant it works perfectly with every device I have thrown at it, from Blu-Ray, to cable boxes, satellite receivers, Apple TV etc.. I also have a 4-way HDMI switchbox to connect 4 HDMI devices to my HDFury.
If you have an otherwise decent HD TV it is well worth getting the HDFury 3. I am just a very satisfied customer.