Acer Aspire 8730-6951 shut-down/ starting/ bios date problem

Here is a new on for you, I have a Aspire 8730-6951 that will not shut-down or power on when it is on the A/C power supply.  It will not even power off when I press and hold down the power button.  It starts shutting down and the screen goes black, but the power button light stays on, the Num Lock stays on, and the cooling fans keeps running.  Also the bios date and time returns to its build date (2008).  If the computer is off and I plug in the power adapter the power button "Blue" light comes on, the battery charge light comes on, and the cooling fan starts running, but the computer will not power up and I lose the current bios date. 

If I unplug the power supply it shuts-down and powers up normally using only the battery power.  So what I have to do is power up the computer using only the battery and then plug in the power adapter, which does charges the battery and keeps the correct time.  Then when I am ready to shut-down the computer I must first unplug the power adapter and then shut down the computer.  When I do this the bios date and time stays correct when I do restart the computer using only the battery.  I can take the re-start option and it will boot down and re-start correctly even with the power supply plugged it. 

I have tried it both without the battery installed using only the power supply, same problem.  I have tried two different power supplies and replaced the bios battery, same problem. I have updated the bios to the newest revision, same problem.  I have tested the CPU, memory, and hard drive; and they all tested OK..  Is it a bad  motherboard???