SQL Server cluster resource won't come online unless its on port 1433
A default instance install (instance name of MSSQLSERVER and on port 1433) will disable the SQL Browser service because 1433 is assumed.  On a clustered SQL install the cluster service will try to connect tot he instance and run a "select @@servername" in order to show that the server is up, but because it's a default instance it tries to use 1433 by default.  I've tried to re-enable the SQL Browser service after changing the port so that the mapping of instance:port happens but haven't had any luck.

What you can try is to set up a client side alias (using SQL Server Configuration Manager) on each node with the virtual SQL name of your default install (the network name) and then put the port number in the alias so that SQLVIRTUAL points to SQLVIRTUAL,3876 or whatever port you are trying to change to.  This way when the cluster service tries to poll the instance to see if it's up on 1433 it will be redirected to the actual port by the alias.  You will not be able to use a dynamic port for this.