Yes and no. You’re entitled to a partial refund if the hotel told you that it would give you one. A review of the Renaissance’s restrictions suggests that you could have canceled your reservation up to a day before your arrival. Otherwise, you would be charged for the first night as a penalty.
You waited until the morning after to take this up with a manager. I’m not sure I would have been that patient. The best time to address a consumer grievance is at the moment it happens – when you can show a hotel employee the red welts that are keeping you awake. The Renaissance might have been able to offer you a different room, or perhaps even a room at another Marriott hotel in the area, in order to make your stay more comfortable.
If the hotel refunded Expedia directly instead of sending the money back to your card, there would have been a little lag time. But how much? It all depends; however, it’s not that unusual to wait two to three billing cycles for the money to appear.
But as a practical matter, Expedia should send you the money as soon as it gets it. If it doesn’t, you could contact the hotel (which you did) and the online travel agency. A written request probably would work best. I list the name, emails and phone numbers of Expedia’s executives on my site: http://elliott.org/contacts/expedia/.
I contacted Expedia on your behalf, and it refunded your room rate, minus $247 for the first night you spent at the Renaissance. When the assistant manager told you he would cancel your “full” reservation, he meant that he would cancel the entire remaining reservation. Had you notified the hotel of your health issues sooner, and checked out before the morning, I might have been able to push for a refund of the entire amount, particularly if a hotel representative had offered you all of your money back. But the partial refund is enough to close this case.