external speakers and headphone do not work at all

Is it a hardware related issue

You can tell whether or not an audio problem is hardware or software by running the Dell Diagnostics audio tests. Use headphones or external speakers while the tests run and if there is no audio through them then it is a hardware failure. To run Dell Diagnostics audio tests

1. Restart the computer and tap the f12 key as soon as it starts to boot up .
2. Select 'Diagnostic' from the boot menu. The computer will run its pre-boot assessment tests (PSA) before Dell Diagnostics starts. During the PSA you will hear some tones through the system speaker but this does not adequately test the audio hardware. Dell Diagnostics plays an instrumental piece of music complete with drums, so if you only hear some tones then you have only run the PSA.
3. Dell Diagnostics should open after the PSA tests, or you should see an option to open it. If you have ever reformatted your entire hard drive then Dell Diagnostics will no longer be there as an option. In that case run it from the Drivers and Utilities (Resource) CD if you have one.
4. Select 'Custom', then the audio tests.
5. The tests will run. You don't need to run all of them. Just check whether or not audio comes through the headphones/speakers during the tests.

If you do hear audio then it is the software and a simple re-installation of the audio driver might fix it. Find the driver in Device Manager and right click on it. Select to uninstall it but not the option to remove it. When you reboot Windows will find the driver files and reconstruct it with its settings set to the defaults, which would allow audio through the output jack if the hardware is working.