normally powered from the main 5 volt bus, thus it coming on when nothing else does is a little odd.
Could be that the power supply comes on with 5 volts and the 12 volts is not coming on.
Re the turn off procedure. When it freezes do you try to turn it off by holding the power button in for 4 to 5 secomds?? That should turn it off. [if it is an ATX type of sustem]
The unplugging and replugging may be confusing things. In an ATX system after the computer is turned off normally [or by holding the power button in to turn off] there STILL IS power applied to the mobo. The power is the 5 volt logic voltage that keeps the system in the mode to be able to turn on by LAN or any of the power management schemes. Any time that the powewr supply is plugged into a live outlet that 5 volts is present on the mobo. When you unplug the AC Power from the supply you remove the 5 volt logic power. When you plug it back in you should wait about 20 seconds before trying to turn on [allows the capacitors to get charged.
In your case it seems that the turn on logic of the mobo is not working properly.
Try the turn off by holding the power switch in for 5 seconds.
Also go into the BIOS and set the power management to user define and then do not enable any of the options. see if that changes anything.
The light coming on while nothing else comes on is definitely unusual.
couple days ago my pc (windows 98 gateway) started freezing up occassionally & only option was to unplug. Well when I plugged back in & pressed power button the light on the front comes on but no fans are running, no sounds at all. I have to unplug & try a couple times b4 it will work. Now I'm waiting for it to come on,,,, the other night it came on about 30 minutes after the power was turned on. Any ideas on help? I appreciate it.