You can't use a splitter to connect two sources to one input. That's the same as connecting the outputs of the PC and TV to each other. You would need an input selector switch to choose either the TV or the PC. You would need a stereo mixer only if you wanted to hear both TV and PC audio at the same time.
If the TV doesn't have an a headphone jack or variable audio output it get more complicated. If the TV only has optical audio output you would need to an optical to analog converter to connect it to the speakers. This output is fixed so the TV remote won't adjust the volume.