To start, I think it's pretty clear that democracy comes in many forms and flavors, and is used on different levels for different purposes. We have referendums that ask voters to decide issues directly. We have elections for representatives that are proxied the responsibility and power to run part of society. In the Iraqi election, voters didn't even get to select those representatives, only parties. So what do all these things that we lump under the common term "democracy" have in common?
To fall back on a psuedo-slogan, it seems like these are all processes that allow "the people" to decide "stuff". The relationship of that "stuff" to "the people" differs depending on the system and it's motivating philosophy. It can range from a referendum asking direct questions to Iraq's election of only parties. Is there a line somewhere for the "stuff," beyond which it becomes too abstract to rightfully be considered a democracy?
Also, do we actually need ballot boxes? What if we have a system where the people express their wills with Gallup polls? What about with armed rebellion? Then it could be argued, what isn't a democracy? What about with money? We consider one-person-one-vote as sacred, but what if rich people think they should have two votes? Some people would say the US is already marching in that direction.
Which brings up the issue of media control in a democracy. As a voter, I get about 100% of my information about an issue or a candidate from the lens of mass media. And mass media needs money. So the naive conclusion is, money control media which controls the electorate. So the people end up being sheep. And they have no choice, I don't think.