I'll assume you're using the TAPCO pre amp to bring the SM58 output up to line level and then sending the mixer output into the sound card line in. If not, then changes things so that's the case and see how it sounds.
Also, try running an iPod or CD player through the mixer (line input) and check how that sounds. If it's bad then the problem is the sound card.
If it's still bad then one or both of the sound card and TAPCO have to go. I have a TAPCO mixer and it's not bad but it's the bottom of the gear range, even though Mackie make it. The pre's are a little noisy. If you think the sound card input is OK and the iPod test is OK, then try a stand alone pre to allow you to boost the mic level before the TAPCO and then run as line level.
The other way is to get a dedicated USB or Firewire recording inferface. I have the M-Audio Profire 2626 which has lot's of ins/outs and good pres. There's a ton of this stuff around to choose from.
Ian
Mu-Theory