Is there no sound at all, or is it super duper quiet?
If the latter, it's probably set to 'digital out', instead of analog.
What's worse is that Realtek tends to hide settings they think you're not using.
So, what you need to do is check first. See if it's set to digital out or analog.
If digital, then look for the analog setting. If you can't find it, then just leave your headphones plugged in, and uninstall the realtek driver. Restart your computer and reinstall the driver. It should automatically detect your headphones and switch to analog.
Let us know if it insists on remaining digital - or if you check the settings and it's already analog.
Edit: one other thing I think you might want to check. If the plug is not seated...