Only just saw this. I'm not sure specifically of any countries that are democratic by my definition. An issue that needs to be fixed, if they want to claim to be democratic, is to have proportional representation - so outcomes don't favour larger political groups; In Canada for example, there are many people who would vote for Green party don't, they vote Liberal say the Conservatives don't get more power. People don't feel safe voting for who'd they vote for because their vote won't count. See http://www.fairvote.ca/ ...
Do you understand the difference between proportional representation voting vs. non-PR voting?
"Democracy is a form of government in which all eligible citizens have an equal say in the decisions that affect their lives. " - Wikipedia
A republic isn't by default a democracy. Non-PR voting doesn't allow all citizens to have an equal say because their vote doesn't count if they vote for smaller political parties; At minimum it's not taking away seats from other parties, and not showing the genuine support for smaller parties -- and the bigger political parties know this and is why they want to keep the system this way.
I figured s/he was making a more nuanced point, e.g. the influence of money in politics, not the one you are implying. Id you are right, I recind my upvote!