It's been said in this thread, but remember unless you're some super special applicant or they are courting you specifically, you're going to have to bend over to their whim.
Three calls each time going to your voicemail doesn't reflect well on you. Then when they call you again to talk about the next step, it again goes to voicemail which sadly was probably the final nail in the coffin. Also, it seems you know that your interviewers preferred method of communication was telephone yet you emailed. I prefer email too, I hate telephone calls/interviews but if that's the way the company I'm interviewing for wants to do it, then I'll live and die by my telephone.
While I don't think you were irresponsible or whatnot, take it as a life lesson. Impressions from things as simple as picking up the phone will matter as much as what you say and how you say it. You could have been a very impressive candidate but it probably irked them they kept getting your voice mail. While you're stating it wasn't always simply that you didn't pick up and there was an outside influence they don't know that and frankly they probably don't care.
I know it sucks to not get the job you want, and even if you had the office visit it doesn't mean they'd hire you. Get a reliable phone, live and let live. There are enough other fritolays-types out there they get applications from and just like colleges they can afford to be picky. There could have been someone just like you as well researched who picked up the phone. Sucks but that's the real world, they'll distinguish you in as many ways as they can and in this case that probably worked against you.