At the start of October I had given a $1400 security deposit for an apartment that I was supposed to move into on November 1st. All of a sudden, something had come up and I am now unable to move in to this apartment. I received this information on October 18th, which is 13 days before I was supposed to move in. No contract or lease was signed and now they won't give me my security deposit back. Is this legal?

The purpose of a security deposit is twofold a) to protect the landlord is there is damage done to the unit and b) to protect if the tenant leaves owing rent.

Even though you didn't have a written lease by tendering the money you committed yourself on a month to month basis. Since you didn't give 30 days notice, the landlord could hold the money as the November rental.