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That's resourceful of you to use that amp to power your speakers - great stuff. Sounds like you're not content with how it's performing, though. That's almost surely due to it being underpowered for you. The front left/right channels of the Logitech system are rated at 7.4 W into 4 Ohms. That equates to about 3.7 W for your 8-Ohm Bose speakers...which isn't much.
That said, a new sound card isn't going to do anything to fix that. Depending on your existing computer audio, that Asus might significantly improve the source material - but it's not going to help power those speakers better. A better amp is where I think you should start, so the option of a used receiver is a great choice. Heck, for less than the cost of that Asus card, you can get a solid stereo receiver such as the Onkyo TX-8255 ($150 at Amazon).