Power Supply Problems?

My computer is attached to a battery back-up, and when it gets close to running out of power it makes a loud high pitched ringing noise. When I'm not home, my parents are computer illiterate/stupid and they just pres the on on the battery back-up to shut it off and stop the noise. Well, that means my computer just shuts off instantly and the whole point of having a battery back-up is gone and out the window. Now, it takes forever before I can start my computer again. Is it the power supply? Please include links and references if possible, or why you think that you know.