Nothing seemed to be leaking while the water was turned off, but the moment Rowen turned it back on, water came rushing down. It was clear that something within the faucet itself was broken. Even though it is a Moen, I did not feel like dealing with customer service agents, warrantees, and the like, so I went to Home Depot and picked out a new model (though still a Moen) and returned home.
There I discovered that the cold water hose (which is a part of the new unit) was a few inches shy of connecting to the water line. Thus, I drove to Trustworthy's and picked up another 3/8ths line (the shortest they had was 60 inches) and a connector. I also picked up dinner from Arby's as the kitchen was not in the proper state to do any cooking and would not be for a little while.
Everything is now hooked up and working properly. However, the process took almost all of my afternoon and evening (largely due to drive times and the time I took picking out a faucet). I really hope that I do not have to do anything like this again any time soon.