Try the obvious stuff first, in case you missed anything. It's easy to do :)

Reboot the computer. Check that everything is plugged in properly, whether it's your speakers or headset. Check that Windows is trying to use the correct device. It may have switched the default to your fixed monitor, especially as you get sound through it. Check the volume for your headset. Windows supports separate volume levels for different devices. Check the headset in the rear connectors on your computer. Check your headset with the cable on a known working device, like your phone. Boot to a live Linux distro and see if the sound works there. Turn the computer off completely, and make sure that you didn't unplug the front panel connector when you installed the SSD.

These should give you a good idea of where the problem is, and let you rule out a few things. Obviously you don't need to carry out the steps that would be redundant, so if your headset works with the rear ports, you don't need to check it with your phone, for example.

Good luck :)