Modem Problem/System Battery Voltage Low Alert

I purchased an older Dell desktop (don't know the model because it's in a different state being used by my mother) a few years ago and recently my mother has been seeing an alert that says “Alert! System Battery Voltage is Low.” at Windows XP startup.  I researched and found out that this may mean that the computer needs a new battery but the strange thing is now that that message is appearing she can’t get on the net using the 56K modem installed in it. Phone line to it is good, has a dialtone, but when she attempts to connect to the net with her dial-up service she gets a “No Dialtone” error.  I must note that the house this computer is in has recently been determined to have bad wiring and other electrical appliances have been on the fritz.  Is it possible that the modem isn’t getting enough voltage to operate or that maybe the modem got fried???