A family of Microsoft relational database management systems designed for ease of use.
Shaunda,
Go to File/Options/General group. Pick a date format that includes the time.
As an update, I did confirm this issue with another experienced user. I will report this as a bug to Microsoft although since it is a minor issue and there are better ways to set the Project start date, I wouldn't hold out any hope for a fix.
Further update: I did get confirmation of a bug in Project 2010 and as I understand it, the same problem also occurs in Project 2013. The bottom line is use the standard method for setting the Project Start Date.
John