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 they 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 them, right click on the "Speakers", only while the headphones/speakers are plugged in, and disable them. This may resolve the issue. Be sure you test that the internal speakers work again, when you unplug the headphones/speakers.
If none of this works to resolve it, you may need to either replace the jack they connect through, or try using a 3.5mm to USB adapter and connect via a USB port.