Can Prism (or InStat) perform Fisher's exact test with tables that are larger than 2 by 2?

There are extensions to the Fisher's exact test for larger tables (larger than 2x2) but Prism and InStat don't do them. You'll need to find another program. 

Here is a web calculator that handles 2 columns and up to 5 rows. 

This page in MathWorld explains how the calculations work, and point out that the test can be defined in a variety of ways, so there is no one right answer.