Assuming you have the correct connections to the TV input, the hum suggests that there might be an earthing problem of some sort. You need to check that there's no potential difference between the earth connection on the PC and that of the TV. Also, the output impedance of the AC97 soundcard will probably be low, i.e. 8 to 16 ohms, whereas the AUX input to a TV or Hi-Fi system will invariably be high impedance, e.g. 50K, 100K etc. A mismatch of this sort can cause significant loss of volume, and at worst, distortion of the audio signal. The fact that it works ok into your amplified PC speakers, shows that the speaker input is matched to accept the low impedance output of your soundcard. Another point worth making here is that you should be using screened twin audio lead between the PC and the TV, in order to reduce mains hum pickup and indeed any other unwanted signals that the TV might be radiating!
As to whether adding a new soundcard will solve the problem, you would need to find a card that offered a high impedance line output. Some older soundcards used to have 4 sockets:- microphone input, line input, loudspeaker output and line output.
Good luck.
ROGER - G0AOZ.