I would hold off on the card for a moment and discuss your sources more. You didn't respond to the suggestion of surround sound headphones, so I'll assume they are off the table and you want a speaker setup.
Is this mostly for music or for music and gaming? If you also use the rig for gaming, then a 5.1 card like the Soundblaster can make sense and we can discuss 5.1 speaker systems to match. It's going to be hard to improve on your speakers with a $400 budget though. For a 5.1 setup you are paying for 5 speakers, a subwoofer and amplification. A Logitech Z906 is closer to $400 new plus the $45 for your Soundblaster. You will likely need to look at the used market to find a 5.1 setup under $400.
If this is for music mostly then your source material will be stereo and you can get better sound with a 2.1 setup like you have now. The built in audio on the Dell 1/8" jack is not particularly high quality, so using an external DAC with your computer's USB port will sound better (no sound card needed). I would recommend a powered speaker like the Kanto YU2 (on sale on Crutchfield for $230)
. These are known to have good audio quality for music but only go down to 80Hz so you will likely want to add a subwoofer. (The YU2 does have a subwoofer output). You could add a Dayton Audio subwoofer from Parts Express for around $155
and be within the $400.
If the budget is tight, Edifier has less expensive powered speakers but not all models have USB or subwoofer outputs (some use RCA in, so you need an 1/8" to RCA adapter, or they use optical or coaxial connections which I don't see on your Dell). You need to look carefully at the features.
Someone mentioned looking for a used receiver and speakers. That can be improved with an external DAC (digital to analogue converter) like an inexpensive Topping or you can use a 1/8" to RCA adapter and connect the PC to any line level RCA input on the receiver. That gives you the option to upgrade the speakers later.
If you go with the Soundblaster, note that you pretty much lock yourself into a computer speaker system like those from Logitech. Only PC speaker systems use the 5 analogue audio outputs on the sound card. Of the 5 jacks, you use the lower 3: stereo front, stereo rear and subwoofer. The Z906 for example includes a 3 connector cable that goes directly from the sound card to the subwoofer and the satellite speakers connect to the subwoofer.