I know it sounds simple, (and you've probably already checked it) but make sure your volume isn't on mute or anything
I've had my fair share of duh moments like that before, and it's always best to start with the simplest possible explanation.
RealTek is just the built-in audio hardware for your computer (and I suspect that your second bullet point "High definition audio device" is referring to that.) Creative SB X-Fi is going to be the good sound card you have installed and are likely using.
Based on Dell's description of your computer, you should have audio jacks in two different groupings in the back of your computer. If you have for sure tried using working headphones in each of these ports without any results, we can be pretty sure that the problem lies with your operating system somewhere, which is good because that means it's probably not faulty hardware. And if the speakers work on another computer then you can be pretty sure there's nothing wrong with them.
If you have a system restore point from before your sound stopped working, and nothing else helps you out, I'd recommend trying to revert to that and see what happens. But save that for later.
Did you install anything noteworthy or make any significant changes to your system or even notice anything unusual within a few days before you starting having this issue?