CPU or MOBO dead??

[#1]

After a house clearence, I was given a laptop, odd make and model, appears to be made by a company called Clevo, which appear to make laptops under various brands.... such as Sagem.  Anyhow, i was going to set it up for the kids to use, but it dosnt start up.  When power is pressed, the CPU fans spin up for a second then stop, and you can hear the HDD operating, but no display or POST, or even POST beeps. I have pulled the HDD, and it appears OK, when slaved to a working system. Even when power pressed, although there is no display or fans running (fans did power up for me once), the DVD drive  ejects OK, and system lights are on. I was thinking that the mobo was stuffed, but I have pulled the CPU and heatsink, and from what I could see, there was hardly any heatsink compound there..... I have redone this, but still nothing. Also reseated the RAM.
I am thinking this is terminal, but I have been told this system was working OK, and I am now wondering if the CPU is fried, dont kow how long the heatsink was like this..n  Its a Pentium 4, socket 478. Dont have one to test with, but  if anyone else also suspects this may be CPU rather than MOBO, I may look around for one. Anyone know how to test CPUs?

[#2]

I doubt it's  the CPU, but it's always possible.
My first suspicion would be the RTC battery,  but couldn't say if it's replaceable on the laptop.
Capacitors also have a tendency  to fail these days which would make the mobo the next like candidate.
Depending on how the system is setup,  it's also possible that the main battery no longer has enough capacity,  but that would only be an issue if the system doesn't bypass the battery when on mains.  That can be tested by removing the battery and seeing if the system still powers up.