Why do I get a series of 8 beeps at start-up?

http://en.community.dell.com/support-for...

The computer might emit a series of beeps during start-up if the LCD cannot display errors or problems. The repetitive beep codes help the user troubleshoot problems with this computer. As correctly mentioned by our esteemed Rockstar, Speedstep in his post above, 8 beeps on an Inspiron N5010 indicates LCD Failure. You have also mentioned that when you connected an external monitor via HDMI, you did not get any display on that as well. However, the system did work fine one time before crashing again.If the LCD on the system does not show and display, here are some basic steps that you perform:

Remove the battery and AC Adapter from the laptop and press the power button down for about 10-15 seconds to release flea power. Power up the system and then press the F12 key during the boot process to get to the Boot Menu, if you are able to see the display. It may be necessary to repeatedly press the key during the start-up process. Use the up and down arrow keys to select <Diagnostics> on the menu and press the Enter key.

Or

Hold down the Fn (function) key Power on the notebook You should then see the Dell logo screen with the message 'Diagnostic boot selected' in the top corner. You can then release the keys

While the LCD BIST test runs, the LCD is operating on its own, free of the video controller, which may be discrete (a video card) or on board (on the system board). The test allows you to distinguish an LCD panel problem from a problem with the controller. If the colors are displayed across the screen without a problem, then the issue is not with the LCD.

I found this video with another suggestion on how to fix your problem.

https://www.youtube.com/watch?v=2Vozz-E7...

Jim