Did the New Deal radically alter American business?

This depends, of course, on what you think of as radical
alteration.  In many ways, the New Deal did not radically alter American business. 
However, if you use the term loosely enough, it did.

The
New Deal did not fundamentally alter the way that American firms did business. 
Companies were not nationalized.  The government did not step in and try to change to a
centrally planned economy.  The US continued to be a market economy just as it had been
before the New Deal.  In that sense, there was no radical
alteration.

You could argue, however, that the environment
that businesses faced was radically altered.  If you feel that the imposition of a
minimum wage or a maximum work week was a radical change, then the New Deal did
radically alter businesses.  The same is true if you believe that the creation of
unemployment insurance was a radical alteration.

So, the
answer really depends on what sort of change you see as
"radical."