Unfortunately, many people just run there dryers without ever having them cleaned & serviced. I suspect that you will find heaps of lint & dust inside especially around the element. Some probably became dislodged during the moving & may now be resting against the element which is giving you the burning smell. Most dryers are reasonably easy to get in to & clean out. Just make sure you draw a diagram or make a note before removing any wires or belt tensioner. So that you can put it back together properly.
Lincoln Appliance NZ
June 2009