I have a Dell vostro 2520 and it does not show any info about starting up on the screen although it makes the startup sound. I have also tried connecting an hdmi cable to an external monitor still no use. Have run the dell PSA as well, it makes the sounds but no display.
Does the system overheat? Were there any bluescreen / system crashes?
Connect an external monitor via VGA cable and check.
When you ran psa - did you encounter any beeps? If so, please specify the exact # of beeps at that would help isolate the source of the issue.
Run the LCD bist - Turn off the system and press and hold the "D" key + power button to turn on the system and it should run the LCD built in self test - see this link for more info - http://dell.to/1SkXNrG
If there is no display on both LCD and external monitor, however, the LCD self test passes, then replace the motherboard.
If there is no warranty, then you could contact our team to get a quote for a paid service call - http://dell.to/1vnT6CQ
My personal suggestion is that you invest your money on a new machine than to repair this system. However, that is your discretion.
Also, please click my DELL-username and write me a private conversation with the service tag and your Name for case records.