Acer Aspire 7720-6569 :: Sudden Shutdown - Power Icon Shows Full Charge And Plugged In

 My battery has not held more than about a 45-second charge since 2009; however, the AC adaptor seems to work fine, and the Power Management icon always tells me that I have a full (i.e., about 45-second) charge and that the AC adaptor is plugged in.  Today, just after I disabled the Acer Tour Reminder, CyberLink PlayMovie, and Microsoft Office OneNote (because I never use them and I wanted a faster startup), I moved some program icons that I didn't need or that were already on my Quick Launch tool bar into the Recycle Bin.  Suddenly, the notebook make sort of an electronic squeaking sound and immediately shut down--black screen; no lights.  
 
I unplugged it, checked to ensure the battery was properly seated, felt to make sure it did not feel hot anywhere, plugged it in, saw that the lights were showing on the adaptor and on the front left edge of the notebook, turned it on, and selected normal start; it started up again.  It ran for at least three minutes (which, because of the battery, it would not unless the AC adaptor was functioning) and then, after I moved a few more icons to the Recycle Bin, it suddenly shut down again in the same manner.  
 
I started it again and it has now been running long enough for me to look up my Acer Forum registration information and update it after resetting my password.  I am writing this on another notebook.  The Acer is still running, but I want to ensure it doesn't shut down on me when I am in the middle of a project.