Welcome to the forum!
There might be a way to set your computer up to do the audio processing and get the 5.1 system working without opening up the other software. If you are getting audio from the center channel, then your computer is already doing some manipulation of the signal. Perhaps the software interface for your onboard sound will allow you to select Pro-Logic decoding or something.
Here's something for you to consider, though. When you connect using the two analog audio outputs from the TV (the red/white jacks), then you can at best have matrixed surround sound (such as Dolby Pro-Logic). Matrixed surround will give you audio in the rear speakers, but it will be a mono signal and will be limited in the frequencies that it will play. In order to get 5.1 audio such as Dolby Digital that has discrete full-range audio in the rear speakers, you would need to use the optical output from your TV.
Also, in my experience, discrete sound cards blow away the sound quality of onboard sound. I'm assuming that onboard sound gets better every year, though, so I don't know how good yours is (likely depends on how good of a motherboard you got).
Adam