What are the signs of CMOS battery failure?

When the CMOS data can no longer maintain info on the bios for example when you look at the date and time let says that your CMOS bios says the following January51997 (System manufactured Date of Mother Board) and time9:00am and you change it to correct information it should stay save by the CMOS by the way if look at the desktop clock time should have change.

Press F1 to boot set up and F2 to Reset Boot Setup ( First boot devices goes to default as F loopy drive

So if u turn your computer the next morning and the date and change again then your battery is weak if not date and time should be same when you change it the1st time. here an article of CMOS battery behavior.

Most current motherboards use a CR20323v Lithium battery for the CMOS battery. The purpose of the battery is to maintain enough power to the CMOS memory to keep the system configuration and clock accurate. It does not get charged up when the power to the motherboard is left on because it is not a rechargeable battery. In the past, many motherboards did use a rechargeable battery to save the CMOS from being lost but this is no longer necessary because modern CMOS memory requires so little power to maintain valid data. A very small battery can be used to keep it valid for months to years. When you replaced the CMOS battery you removed the old one which caused your CMOS to lose power and, therefore, the data and the clock became invalid. Then you installed the new one which restored power but did not restore the lost data or clock. So when you powered on the system the CMOS data was again in the invalid state and needed to be rewritten by the BIOS program. All of this is normal and does not indicate a problem with your motherboard.However, the following statement, "Everything was fine except I could no longer see any icons in the notification area. Changing the Bios date/time didn't seem to do anything as the PC's system date was still wrong; off by about a year.", could possibly indicate a problem, most likely with windows. I have seen this particular issue myself several times after I have been working in the BIOS. Windows, for reasons that I have never understood, sometimes fails to update the date/time correctly. I wouldn't worry too much about that as long as the date/time stays current and correct after you set it in windows.. However, the fact that you lost your icons in the notification area suggests that something got corrupted in Windows. Which version of windows are you running? Can you describe in better detail what exactly you're not seeing? Is it just the icons or is the entire notification area missing? I assume you're referring to the small area in the lower right hand corner next to the date/time display, correct? Does the rest of your Desktop come up OK? Does your Startup menu appear correct or are there items missing? Also look at the devices in Device Manager to see if there are any devices that are not working or cannot start.

The word CMOS is an acronym for “complementary metal oxide semiconductor”.
The CMOS battery is a small, round battery that lets you store the day, time, and month on your computer.
It allows you to shut your PC down for an extended period of time and still have the correct time and date in place when you use your PC again.
More importantly, the CMOS battery stores the BIOS settings of your computer.
The BIOS enables us to identify what hardware is on the system and what device drivers to use.
When the CMOS battery is weak, the BIOS loses data and the computer can start to malfunction.
Let’s take a look at a few signs of a CMOS battery failure.
Incorrect computer date and time settings.
Also, the date/time keep getting reset even after you fix them in the BIOS.
This is the most common CMOS battery failure sign.
Your PC occasionally turns off or doesn’t start.
Drivers stop working.
You may start to get errors while booting that say something like “CMOS checksum error” or “CMOS read error”.
Some weird hardware issues such as your computer not being able to locate the mouse, keyboard, or printer.

If your computer is losing its time or date settings, or you are receiving a message CMOS Read Error, CMOS checksum error, or CMOS Battery Failure you are in big trouble

If Your CMOS ( Complimentry Metal Oxide Semi-conductor) is failure then the P.C is not show correct Date & Time. As well BIOS ( Basic Input Output System ) Does not Work Properly. Becouse of CMOS Battery provide Current to the BIOS. So that BIOS will not keep all the Infomation about all Hardware Devices of System. And System may be restart again and again and system will give BIP sound

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The most common symptom if your CMOS battery is already dead is the setting clock of your PC/Laptop will go back to the original date of manufacturing of the motherboard.
Another is the error message will pop up as stated answer from other members.

The Bios setting are changed every time you restart or when you shut down and put on computer. 

common are date and time.

- Computer date will be on post date .
( Like manufacturing date of Motherboard) - Press F1 to boot ( First boot devices goes to default as F loopy drive) no more than these issue will comes if CMOS battery failure Solution Change CMOS battery and change date and Boot priority )

The answer is no1

When you power On your System and then, it's stop and appeared “CMOS checksum error” or “CMOS read error”.
That means you have CMOS fault.