I had this problem in my last job. I tried everything -- asked for more work, helped other people, worked on my skills. When I still wasn't busy, I surfed the internet, read books, listened to music. As time went on, I was getting in later and later and sometimes leaving early. I worked at home one day a week and sometimes I had nothing to do on that day, either, so I would sit and wait for emails from work. When I had work to do, I would do it v e r y s l o w l y unless there was some sort of tight deadline.
I was going crazy. I suggested changing my job to part time, but they didn't want to do that. I finally resigned, and I guess you'd say I'm retired now. So maybe it was just as well that I wasn't busier, or I'd still be there. And the work didn't exactly excite me.
What is it with all these places that hire full-time workers who sit around half the time doing nothing? I don't get it.