You probably have a bad torque converter, every time you engage a moving gear, your torque converter is supposed to "free spin" the transmission when the engine is at idle. It doens't sound like it is doing its job.
The 2011 Toyota Corolla has front wheel drive.
The 2005 Toyota Corolla has front wheel drive.
The 2012 Toyota Corolla has front wheel drive.
The 2002 Toyota Corolla has front wheel drive.
The 2010 Toyota Corolla has front wheel drive.
The 2007 Toyota Corolla has front wheel drive.
The 2006 Toyota Corolla has front wheel drive.
The 2013 Toyota Corolla has front wheel drive.
The 2014 Toyota Corolla has front wheel drive.
The 2003 Toyota Corolla has front wheel drive.
The 2001 Toyota Corolla has front wheel drive.
The 2008 Toyota Corolla has front wheel drive.