The installation wizard asks for an Activation key (that is 20 characters long (e.g. ABC12-EFGHI-34JKL-MN56O)) when I have an Product key (that is 12 characters long (e.g. ABCD-1234-5678)).

Make sure that you have downloaded the correct version of SIMCA/MODDE, if you have a product key you should use the following links
For MODDE 9.1 http://www.umetrics.com/download-software
SIMCA 13.0/MODDE 9.0 and older versions, http://www.umetrics.com/default.aspx?id=9537