Removing battery to boot up laptop

I have a four yr. old Inspiron 9100.  Recently, after shutting down for the night, in the morning, when I press and hold the button to boot up, I hear something coming on, but the screen stays black and nothing really happens.  I called Dell Tech support, and they told me to turn it off, remove the power cord, remove the battery, then put the battery back in, replace the power cord, and turn it on.  It worked, but she never said what was wrong.  Now, everytime I shut it down, I must remove the battery and put it back in just to get it to come on. I rarely use the battery as the laptop it plugged in to AC outlet 99% of the time.  Should I remove the  battery and just leave it out, get a new one, or what?  Obviously, something is wrong, I don't want to have to remove the battery and put it back in every day.  Any advice is appreciated.