Re: Clock on my computer shows incorrect time.
The battery should keep the basic mainboard functions going for a very long time, how old is it?
Have you tried clicking on the clock (right lower corner -> Change Date and Time Settings -> "Tab: Internet Time" -> Change Settings -> Synchronize with an Internet time server.
When you shut down, and restart your system after about 10 minutes you should be able to determine if the time is wrong or not.
X: If it is -> Change Mainboard battery
X: if it is showing the correct time -> Well, that would be it. Problem solved