tl;dr: I'm a student, the university does not push basketball the way they do football, and that's why students don't show. Also, we don't remember the good times the way y'all blue-hairs do.
Since at least part of this thread has turned into criticism of the student section, I thought I could offer my take since I, you know, sit in the student section.
1. Unless you get there early, our seats suck. I think you guys recognize this. Just look at places like Michigan State where the student section practically wraps around the entire court in the bottom 10 or so rows. Getting loud students near the court could help with the noise issue. I suppose the drawback to this would be that it could look bad on TV if your students don't show, but maybe a couple other of these points could fix that.
2. Honestly the season ticket is fairly cheap compared to what you would pay if you weren't a student, but it could be free. I don't want to sound like someone asking for a handout. I pay for the ticket anyways since I have always been an Iowa fan, but basketball has a student attendance problem. No one is sitting there anyways, so just give the damn tickets away. Perhaps you could do a tiered structure where you pay to guarantee your student ticket (which, being the sucker I am I would pay for it), and after a set period of time, you open it up for free until you run out of tickets. I would also pull a United and give away more tickets then there are seats just to make sure we get people in. We got a huge-ass concourse you can watch the game from if you show up late and can't find somewhere to sit.
3. People my age and younger don't think of Iowa for basketball. Just about the earliest I remember is the year Iowa lost to Northwestern State. And even then, as Iowa fans, we try very hard to erase the tenure of that head coach from our memory. The fans my age just aren't there for basketball the same way they are for football. If you're my age you remember back-to-back-to-back top 10 finishes in our formative years. Basketball doesn't have anything like that.
4. The school doesn't push basketball at all. Campus grinds to a halt on fall Saturdays. More than 9/10 students couldn't even tell you if there was a home basketball game tonight or not. You hear all about football during On Iowa (orientation) week. Not a peep about Basketball. Somehow even less about Wrestling. I bet most students would be surprised about how good of a wrestling tradition we have.
5. Finally, there is a growing number of people who simply don't care about athletics. Couple this with a growing number of out of state residents who don't grow up Hawks, as well as no push to get you to attend basketball, you end up with an apathetic student fanbase.