Hi,
Have you checked that the laptop is actually off and not just in sleep mode or hibernation?
Try holding the power button until the laptop shuts down completely and then check what happens.
Have you checked all the sleep setting options in Control Panel > Power Options > Change Plan Settings > Change Advanced Power Settings > Sleep to make sure that they’re what you want?
@James Pontius ,
Did you check the Advanced Power Option sleep settings, you didn't say?
Did you check any of the settings in the Power Management section of the BIOS e.g. AC Behaviour - especially wake on AC or Wake on LAN/WLAN, Auto On Time or USB Wake support to see if they may be set so as to cause the problem?
Here's a link to the owner manual scroll to p.50 to view the default settings for all the above Power management settings.
Did you try a power refresh to clear the BIOS back to default values.
This should have happened when you replaced the CMOS battery assuming you had the main battery out at the same time but maybe you were too quick.
Try removing the charger (if connected) the main battery and the CMOS battery and then hold the power button operated for 30 seconds to dissipate any residual power from the laptop and then release the button. Replace all the batteries and then check what happens