how can i findout if my laptop cpu has packed up?

I have a laptop that is about 3 years old now. It started becoming difficult to boot up and this problem was intermittent for a few weeks. It now won't boot up at all. You can hear it trying to read the CD Rom drive because it clicks so I don't think its the CMOS battery. I can also hear the fan on the heatsink coming on when it tries to boot then shuts off again. I get nothing at all just a black screen and it just goes through the boot sequence over and over again.

I wondered if anyone has any experience of this particular model as I would like to try to repair it. I suspect its the CPU as the laptop used to get extremely hot. It would appear that its a common fault as I noticed when looking on ebay for a second hand CPU, someone else was selling the same laptop for spares or repair with exactly the same fault.