First, you need to be aware that if you are using Toslink or digi coax, then you are bypassing the DAC in your soundcard, and therefore you are not getting any benefits from using a fancy sound card at all. You could get the same quality audio by taking a Toslink or digi coax straight off the integrated mobo audio in the digi domain and passing that to your external DAC. The way you describe your setup, it seems that you are using the DAC in your Logitech speakers.
Next item, you don't want to use computer speakers in your car. You want to use car speakers in your car. Use the computer as the source component, then send that to a head unit and use the head unit to distribute the audio and control the volume and the subwoofer-- and for the subwoofer you again need a sub designed for cars and you will want a dedicated sub amp for the best performance.
But, you left out some very critical details here! What is the make, model, and year model for your car? Depending on that info, the install could be fairly simple or could be nearly impossible, or at least so much work that it just isn't worth it.
Finally, you are going to have to figure out exactly how you are going to power up your computer in your car. Your car is going to be a 12V system. A computer needs several different voltages to operate. I can't remember them all off the top of my head, would need to look into that. In the home computer, the PS plugs into the wall and provides several different output voltages for different circuits. You are going to have to figure out exactly how you are going to generate those different voltages in the car 12V system. That will not be trivial!
So, what you propose is absolutely possible, but this will not be an easy task by any means. Also, understand that there is some risk involved here, and if this is your first project of this type then the risk is even greater.