I just encountered someone who had grasped that the problem was wealth inequality combined with the fact that wealth is power but who had not reached the conclusion that socialism was necessary, so I wrote this, which is a pretty succinct summary of my own current political views. Lots of links to elaborate on each part.
The problem is capitalism, which invariably concentrates wealth.
We cannot correct this problem under capitalism because as you noted, wealth is power, and there will always be concentrated wealth under capitalism, so capitalism is inevitably a plutocracy, a class society.
Capitalism is any mode of private ownership of the means of production where production is primarily driven by profit, which will inevitably be a chaos of production. The only alternative is a democratically controlled planned economy, socialism.
Many countries have tried to peacefully arrive at socialism with unarmed movements, including Guatemala from 1944-1954, Chile from 1970-73, Jamaica in the 70s, and Grenada from 1979-1983. These explicitly socialist movements, and all unarmed anti-imperialist movements that attempted to secure gains for a Third World country’s workers and peasants even when not attempting to overthrow capitalism, have been destroyed and subverted by the CIA and its allies.
The only solution is socialist revolution, country after country, from the bottom of the world to the top. Right now there are armed movements to bring about socialism in various places, most notably India and the Philippines.
Because it has been observed that high food prices (and high costs for other necessities) spark revolutions, and because much of the world is soon to be short on oil (and many other resources) and water, and therefore food as well as most other things (because oil is used to ship things), we should expect revolutions all over the world in the near future.
If we want to bring about a just, free, and ecologically sound world, we must support those movements and prepare for our opportunity to bring socialism to the imperialist countries such as the United States.
It is tragic that it should have to happen that way, but the world right now is a tragic place, where 7 million starve to death every year, tens of millions more die of easily treated diseases, and 2 billion live on less than a PPP-adjusted $2 a day (that is, on what you or I could buy with $2), and the wealthy, whom you have correctly identified as the ruling class, profit off of this and will do everything in their power to perpetuate it. And what’s more, humanity itself is doomed without a solution to global warming and other ecological problems, which can be solved only with global socialism.