Dell Inspiron 1525 will not boot up - please help!

Hello, I am hoping someone can help me as my computer is out of warranty.  On Thursday, my Dell Inspiron 1525 (bought in 2008) running Vista Operating System was working perfectly.  No issues at all.  On Friday morning, I went to turn on the computer and the 2 blue lights on the bottom left (the power and the one beside it) light up, the computer sounds like it is going to boot and then it beeps once and dies.  It will continue to do this over and over every few seconds until I turn off the power manually.

I have tried the trick of taking out the battery and the cord, pressing the power button and then plugging the battery and cord back in, but it still did not work.  The computer will not boot using just the cord (and not the battery) and vice versa.  Does anyone have any ideas on what could be happening or how I could fix this?

Thank you in advance for any help you could offer.