You say analog like it is a bad thing
Even if you where using digital output you would still have to convert it to analog before the speakers play it.
I guarantee you that even your computers cheap audio codec has a better DAC than any set of Logitech speakers...
A real sound card would defiantly give you much better sound quality.
Unfortunately, it probably will not stop the speakers from hissing.
Do a quick test and see if a new sound card will fix your issue.
Next time you are sitting at your computer, you have nothing playing and you hear the hissing, unplug the speaker jacks from the computer.
If the hissing goes away, it was interference from your system and a quality sound card would probably help.
If it does not go away, you just have a noisy amp and a new sound card would not help.