Check the reading of the power button LED, is it Steady Blue, Blinking Blue, Steady Amber, Blinking Amber?
As there are 'Beep's', please post the sequence of them?
The Inspiron 531 Owners Manual and Troubleshooter is HERE
As shesagordie correctly said, we need to have the sequence of beep codes or the Power button status to isolate the issue further.
Kindly post back the results so that I can help you isolate the issue further.
Awaiting your response!
Two 'Beeps' indicate a memory issue, try opening the case, then remove and reinstall all the memory modules and see if this makes a difference.
The procedures for this are in the link I've already posted.