The New Deal clearly did not end the Great Depression. The New Deal definitely ameliorated the problems connected to the Depression, but it definitely did not end the Depression.
We can tell that the New Deal did not end the Depression because unemployment levels and GDP levels did not return to pre-Depression levels during the time of the New Deal. Instead, they only returned to those levels after 1939. What really got the economy back on track, sad to say, was World War II. With men getting drafted into the military (even before war was declared) and with factories ramping up production for the US military and for Lend-Lease, the war was a huge boon to the US economy.
The Depression would surely have been longer and deeper if it had not been for the New Deal. The New Deal provided relief to people in need and started the US economy on the way to recovery. However, it is not at all clear if it could have gotten the economy back to pre-Depression levels had it not been for the war.