Motherboard keeps giving checksum error after installing new battery

I am repairing a computer with an ASUS M2NBP-VM CSM ACPI motherboard (I am not sure this is the correct description of the motherboard but, at least, this is what gets printed to the screen during boot).

During boot, I get the following error message:

CMOS checksum error - Defaults loaded

Indeed, the time, date, and boot device priority are reset and the values I had set up before switching the computer off are gone.

My first explanation was that the CMOS battery must be empty so I bought and installed a new one. But the behaviour has not changed: after switching off and disconnecting the power cable, the next time I switch on, the CMOS settings are lost and the error message is printed again.

Any suggestions as to what I should check next?

EDIT

Following the suggestions contained in the answers and comments, I performed a few further tests using another computer that I know is working properly, i.e. it does not lose BIOS settings between reboots.

1. Unplugged computer with its own battery on, waited a minute or two, plugged again, booted: settings are there.
2. Unplugged again, removed battery, put new battery (the one I had used to test the bad computer as described above) in, plugged in, booted, set up time and date, shut down, unplugged, waited for a few minutes, plugged, booted: settings are there. So: the new battery is good.
3. Unplugged again, removed new battery, put old battery from bad computer in, plugged, set up time and date, shut down, unplugged, waited for a few minutes, plugged, booted: settings are NOT THERE. So: the old battery is bad.

So, I have ruled out the case that the new battery is bad. I have performed another test on another computer I am trying to repair. Same model as the bad one above. Removed battery and put the new battery in: it does not retain the settings. The reset jumper is also in the proper position (no reset).

So the problem must be in the main boards. Since I would find it unlikely that they have both broken in the same way, I guess the only test left is to flash the firmware on the main board. Only, I do not understand why this should work: the old firmware has worked before, why should the old firmware have stopped working at some point?