I've been busy lately and not keeping up, so I'm jumping in late. I have a Fiji card, which is more or less the same as a Pinnacle.
For the distortion problem, make sure you have all your levels set right. First, set the gain (trim) on the mixer channel input. Talk into the mic or play the instrument or whatever, and make sure the output from the mixer is not clipping. Then, open up the mixer application for the Pinnacle card. When you talk into the mic you should see the input level meters for the CD/Line input lighting up. Make sure the faders here are set so that the input level is staying below red at the loudest volume you expect to record. (Remember that the soundcard input is an analog-to-digital conversion. So if you clip, it won't be a warm, analog type of clipping. It'll be an ugly clipping. So you never want to go above 0db here.) Finally, while talking into the mic, check out the input level meter in the Cubase channel you're recording into. Make sure the level here is not too high.
So, all three levels---mixer output, soundcard input, and Cubase input---must not be clipping.
As for connections, it sounds like you have the output from the sound card connected right. Connect the Line Out from the sound card to two of your mixers input channels (or one stereo channel if you have it). Then, as you said, you can monitor this from the control room bus.
For the soundcard's Line In, you have several choices. There are some minor pros and cons to each method.
1.) You can connect the Line In to the Direct Out jack of the mixer channel you want to record (that is, if your mixer has Direct Outs). The advantages are that the sound is not going through the whole path of the mixer and you're theoretically getting a slightly cleaner signal. Also, you'll still have the use of the mixer's EQ controls to touch up the sound. The disadvantage is that if you want to record some other mixer channel, you'll have to unplug the cord and move it to the other channel. Also, you cannot record multiple channels at once, such as in recording a whole drum set with multiple mics.
2.) You can connect the Line In to the Insert jack of the mixer channel you want to record, as Track Rat mentioned. This gives you an even cleaner signal than using the Direct Out method (theoretically) because the signal doesn't go through the whole path of the mixer channel. But then you don't get the benefit of using the channel EQ, mute button, or fader as you did using the Direct Out. The disadvantages are the same as the Direct Out method above.
One thing to watch out for here is how far you push the plug into the Insert jack. I have a Mackie mixer. In the Mackie, if you push the plug all the way in, you cut off the signal from going any further in the mixer. I wouldn't be able to monitor my own voice through headphones as I was recording. So I'd want to push the plug only halfway in (one click). Your mixer might be different. Check the manual.
3.) You can connect the left and right Line In to two Aux Send outputs of the mixer. The advantages of this method are that you can decide which channel to record with out re-plugging any cords, and you can easily record multiple mixer channels at once. You can also easily direct the sound to the left or right side of the sound card, which you can't do with the above methods without re-plugging the cord. Plus, if your Aux Sends have a pre/post button, you can easily choose whether you want to use that channel's EQ and fader, or whether you want to avoid the EQ and fader to get a shorter signal path and a cleaner signal. I think using the Aux Sends is a more flexible way to go than the first two. The disadvantage is that you are tying up your Aux Sends which you may want to use for effects instead.
If you use this method, there's one thing to watch out for. Remember that the Line Out of your sound card is going into two channels of your mixer. Make sure that the Aux Sends on these two channels are turned all the way down. If you turn them up, you'll be feeding you previously recorded stuff back into the soundcard input and you'll create a loop.
4.) You can connect the Line In to the Group 1+2 or Group 3+4 outputs of the mixer. This is the way I currently have mine set up. The advantages are that you can record multiple mixer channels at once, and you can use the channel EQ, mute and fader, of the channels. Plus, you are not tying up your Aux Sends, so you can use them for effects. In fact, if you have a button that directs your Aux Returns to the Group 1+2 mix, you can choose to add effects to the recorded signal without re-plugging cords. The disadvantage of this method is that the sound is going through almost the whole mixer's signal path (you've added the subgroup mixer stage). This is theoretically not as clean. But for me, I don't worry about it. I have other sources of noise that are probably worse than this.
Again, check those two channels coming from the soundcard's outputs. Make sure they are not patched into the Group 1+2 or you'll get a loop.
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There may be other creative ways to connect things that I haven't thought of. There are other places on your mixer you could connect your sound card's outputs, too. If you don't want to tie up two of your mixer channels to monitor the previously recorded stuff, you could connect the soundcard outputs to your Tape In jack. Or you could connect them to an Aux Return. But this is getting way to long, so I won't confuse the issue any more.
I'm not sure I understood your last question. Are you asking what is the advantage of hard disk recording vs. recording to tape? If so, the advantage is that you get great sound quality for the price. Also, when you record to hard disk, you can edit and manipulate your recordings much easier. (This is another big topic)
Jim