CMOS Checksum Error

I'm helping troubleshoot a CMOS checksum error they are getting on their Inspiron 546 desktop. The date and time are lost every time the computer is turned off, so we started with replacing the battery. The date and time are still lost every time the computer is turned off with the new battery. Thinking the new battery may also have been dead, the voltage of both batteries was checked, and is reading 2.8 to 2.9 volts. Other than getting the error message, entering the CMOS setup and then exiting without saving changes, and having to set the date and time every time the computer is started up, everything else with the computer seems to be fine and functioning normally.

Something I've noticed is that every time the computer is restarted, the date and time are not reset to the same default date and time. For example, one time it was 31 Dec 2001 11:00 PM, and the next time it was 3 Jan 2002 10:00 PM. I'm wondering if this could be a clue as to what may be causing the issue? I would have expected it to reset each time to the same default date and time if it is not detecting battery power, but perhaps I'm misunderstanding.

I know from reading the manual that the CMOS checksum error can also indicate a problem with the motherboard, but there is nothing obviously wrong that I can visually detect. Any ideas as to what else I can try to troubleshoot this problem are greatly appreciated. Thanks in advance.