The Austrian school is a valid economic school that is too often ignored in favor of Keynesianism, which history has shown not to work. Take, for example, the United States' crashes of 1920 and 1929. In 1920, the US government cut it's budget, as Austrian economists recommend, and the young Federal Reserve did the opposite of what Keynesian economics recommends. Despite the fact that the crash was as bad as the one that would happen 9 years later, that economic downturn ended in 1921. In 1929, on the other hand, the government increased spending on bailouts and public works projects (not just under Roosevelt, these programs began under Hoover), and the Federal Reserve acted as Keynes recommended. It took World War II to end the resulting depression. By killing millions of people, and employing most of the country either in the army or making weapons. So it was not exactly an optimal situation.
Edit to respond to edit: I'm sorry, but if Paul Krugman is as deep as you've looked in economics, you need to look deeper, whether it be on the Keynesian side or [preferably] on the Austrian side. Krugman is not consistent and not above average as economist. He excels mostly at being very stuck-up. One search for "Paul Krugman refuted" and I found
this gem about how Krugman laughed at the idea of even considering a particular aspect of Austrian theory, and a few years later, accepted it.
Historical examples, such as the crashes of 1920 vs. 1929, and every bubble that has occurred since (Austrian economists accurately predicted the housing bubble long before anyone else did, this is because of the Austrian theory of the business cycle, or the "hangover theory"), show that Austrian economics at the very least is worthy of consideration and indicate that it is the economic theory with the most real-world evidence supporting it.
Whether or not a theory is the "accepted theory" should not be your only marker in considering its validity. When Copernicus asserted that the Earth orbited the Sun, this was not the "accepted theory."
In economics, almost everyone has a bias, because they have something to gain from the acceptance of a particular economic theory. Keynesian theory benefits mostly the financial institutions that are paid by the government. It also benefits employees of the Federal Reserve, since it keeps them in business. Austrian theory benefits mostly people who would like to get what they earn and keep what they earn, and people who save money (because the use of QE and other methods of producing inflation harm those who save by devaluing a currency).
Do not accept a theory only because a majority does, accept a theory only after looking at its actual validity and the biases of those promoting it. Keynesianism may be the majority accepted theory, but it is not necessarily correct, and history shows it.
Disclaimer: I am not an economist. However, I have taken interest in economics ever since reading what Austrian economists have to say about the basic fallacies of Keynesian theory, and am learning economics. I know enough to provide a few examples, but if I have made an error, do not necessarily hold this against Austrian theorists, as I do not claim to be one.