If you can hear music and its not all distorted you do have a phono preamp somewhere (I'm sure you know this already). This probably isn't it, but I know some Technics TT's have their own built in phono preamp. If yours has one, connecting it to the phono input on your amp would not be a good idea. Then you would be using 2 phono preamps. If your not at all sure, just connect your TT to a different input and see what happens. You can't do any damage by trying this. Actually, if your TT does have its own pre, connect it directly to your sound card.
Beyond that, you may want to have a look at your software settings. Check your global gain settings for whatever OS you are working with. I make that mistake myself all the time. One last thing you may want to try is to connect your TT directly to the sound card even if you don't have a built in phono stage. Your cart is almost certainly a high output MM. I'm pretty sure you can find a RIAA EQ curve plug in for Audacity. If you can get that EQ curve, your sound card may have enough gain to make it work. Understand, though, this is just a guess on my part. I've never done this but I know your sound card is very good and may have enough clean gain to do the job.