Acer Aspire dead on start-up, then it isn't

Can anyone help me with a hardware issue? I have an Acer Aspire M3201 that has developed a start-up problem. This runs the AMD Phenom 8650 triple-core CPU and my diagnostic software identifies the motherboard as ID9600.

Until a few days ago the computer has always worked flawlessly. Then suddenly it wouldn’t start. I checked the PSU and that is okay but no other sign of life except the fans. The power switch has a light that normally comes on and it also was dead. I tried switching the computer on and off many times in many different ways and nothing. Also nothing from the BIOS. Then, after many attempts, the power light suddenly came on and the computer started normally. I ran it all day without any issues.

While it was working I tapped around the motherboard looking for bad connections or chips but everything seemed fine. Eventually I shut it down. The next day exactly the same thing happened. Dead as a dodo. Again, I tried tapping around the motherboard while attempting to switch it on but no response. Finally, after many, many attempts, it suddenly came on and worked normally.

This morning when the same thing happened again I had a bright idea and tried warming the motherboard with a hair dryer. This time it turned on after only a few tries. I have only done this once so can’t be certain that it is temperature-related, but that certainly seems possible.

I know some basic electronics but not enough to diagnose this any further. Has anyone else experienced anything like this, or does anyone have any idea what might be going on? I use this computer a lot and the OS is locked to it, so I would really like to fix this if at all possible. Any suggestions would be much appreciated.