The auto start might be a BIOS setting to auto start after power loss. If this is set then it would try to turn itself on after any indication of a power loss.
The 3 or 4 second issue reflects the fact that holding the power on button for 3 or 4 seconds is designed to shut off the computer. If the BIOS is reading this as a power failure then the BIOS would try to turn it back on.
When you say you put it into it's hole it again raises heat issues.
Overall there is a growing suspicion in my mind of the PSU.
You can get a PSU tester at most any computer store such as:
LCD Power Supply Tester : PSU Tester : Maplin