I'm flying in as well.
Like LeeAllure said, there is a train that goes from the airport to Norrisnown.
Here is the website for the train system:
http://www.septa.org/service/rail
Take the Airport line to the Manayunk/Norristown Line.
Also, I did not know there is a shuttle from the train station to
the hotel. Thanks for that, LeeAllure!