If your external speakers/headphones aren't working, try the following...
1. Go to "Control Panel".
2. Click on "Sound".
3. Make sure you are on the "Playback" tab.
4. Click on the device you are trying to fix.
5. Now click the "Configure" button and follow the prompts. (Be sure you also click the "Test" button.)
6. Once that is complete, click the "Properties" button.
7. When you are done with your changes, in "Properties", click "Apply" and then "OK".
8. Then click "OK", again, on the main "Sound window".
NOTE: If the headphones don't show in there, right click on the white background of that window and make sure both "Show disabled devices" and "Show disconnected devices" is checked.
Should you still not see the headphones, right click on the "Speakers", only while the headphones are plugged in, and disable them. This may resolve the issue. Be sure you test that the speakers work again, when you unplug the headphones.
If none of the above works, I would take the laptop back and get them to replace it as it has issues.