Hello.The problem could be either in the hardware or the software, so you need to test each. Perform the tests below -- it doesn't matter which one you do first.
To test the speakers, perform the Quick Audio Check in the ePSA test. If the speakers fail the test then they have failed or become disconnected. (Click the link for instructions on how to run the test.)
To test the software, switch between the Realtek audio driver and the Windows native driver. [This test assumes that your laptop has the Realtek audio driver. If you get to step 2 and do not see "Realtek High Definition Audio" then go to the Dell support page for your model and download the Realtek driver that Dell provides for the version of Windows that the laptop is running.]
1. Open the Device Manager (find it in the Control Panel, or type devmgmt.msc into the search box).
2. Expand the "Sound, video & game controllers" and right click on "Realtek High Definition Audio".
3. Select to "Update Driver Software".
4. Click on "Browse my computer for driver software".
5. Click "Let me pick from a list of drivers on my computer".
6. Put a check in the box "Show compatible hardware" if not already checked.
7. In the list of devices, click "High Definition Audio" (the native driver).
8. Click "Next".
9. On the Update Driver Warning box, click "Yes" (install the driver).
10. Restart the laptop if prompted. If not prompted, then no need to restart.
[To get back to the Realtek driver, do it again but reverse the names in steps 2 and 7.]
If the speakers work correctly only with the native driver, then the Realtek driver is buggy. If the speakers work correctly only with the Realtek driver, then the native driver is buggy.
If the speakers worked during the Quick Audio Check (above) but do not work with either driver, it could be that the sensing mechanism in the headphone jack has failed, making Windows think that there is a plug in the jack when there is not. There is a full explanation of that issue in the Headphone Jack FAQ.