Is there integrated audio (built into motherboard)? If there is, try disabling it from the device manager (right-click My Computer > properties > hardware tab > device manager). To disable (right-click > disable).Make sure that the new audio card is showing up right (ie: no “!” or “?“). If either symbol shows up for anything listed, either re-install the device driver, or find a more compatible driver.
Chances are, the old audio is still the dominant driver in this situation. The sound card should automatically disable the on-board audio, forcing Windows to use the sound card. If the on-board driver is not disabled, try manually disabling it (right-click > disable) in device manager.
Also double-check the audio connections again in the back. More often that not, people plug their speakers into the mic outlet or something to that effect by mistake.