For a 4 year old laptop I shouldn't spend too much money. It's either the motherboard or the CPU (or possibly the PSU giving not enough power, but that's rather unlikely). It's up to you if you start testing the CPU with another motherboard or the motherboard with another CPU. It's even up to you to decide if it's worth the risk to spend mony with the risk the final solution is too expensive.
I've got a acer aspire 5750 that is starting for 1 second before it shuts off again. I've stripped the motherboard out for testing purposes and at the moment all I've got connected is the CPU and a stick of memory. I've tried starting the laptop with no memory and also with a different stick of ram but still no luck.
The cpu fan spins for that one second before it all shuts down.
Also whenever I plug in the power cord into the power jack the mother starts automatically (not sure if this meant to happen)
What could the problem be? I know the motherboard has power running through it so could it be the CPU?
Any troubleshooting or help would be appreciated!