New Deal was awesome. It only took six years of its brilliance to get
the unemployment rate down to 19%. (My favorite part is when FDR would
wake up in the AM and just decide to move the price of gold around.) Good news for people who feel the need to be partisans: the New Deal makes Obama and his Congresses look like economic wizards.
It is certainly correct that the Great Depression is not a full test of Keynesian econ, given all of the other govt interventions (by Hoover-- far from a free-market type; and more famously, FDR) and non-Keynesian policy failures of that time (policies that would have concerned Keynes with respect to Macro): wage and price floors, dramatically strengthening labor market cartels, catatonic monetary policy, etc.
People often forget the tax increases of the Great Depression-- in particular, the new payroll tax on labor in 1937-38. It's funny: when you tax labor, firms don't want to use labor as much. Weird, huh?
Keynesianism has been intellectually bankrupt (in Econ) since the early 1970s. (Believing in old Keynesianism is akin to believing atavistic theories of criminal justice. "New Keynesianism" is far more respectable.)
On the claim that WWII fixed everything:
1.) It's always fun with people advocate war to fix an economy.
2.) There's certainly a sense in which the claim is true: when you have surplus labor, you can reduce the surplus by conscripting a ton of people and sending them to fight.
3.) One of the tough nuggets for K was the failed predictions of economic calamity when the WWII spending went away. It is a sad mark for the profession that Keynesianism didn't take a fatal beating until years later.