DateTime objects have a "Kind" variable which helps TimeZoneInfo know how to treat it. In the MSDN documentation for TimeZone.ConvertTime it has the following:
DateTimeKind.Local, Converts the local time to the time in destinationTimeZone.
DateTimeKind.Utc, Converts Coordinated Universal Time (UTC) to the time in destinationTimeZone.
DateTimeKind.Unspecified, Assumed to be Local.
For example:
  Console.WriteLine("Local time zone is '{0}'.", TimeZoneInfo.Local.Id);
  var gmTime          = new DateTime(2013, 03, 02, 01, 00, 00, DateTimeKind.Utc);
  var localTime       = new DateTime(2013, 03, 02, 01, 00, 00, DateTimeKind.Local);
  var unspecifiedTime = new DateTime(2013, 03, 02, 01, 00, 00);
  var timeZone = TimeZoneInfo.FindSystemTimeZoneById("Eastern Standard Time");
  var gmTimeConverted           = TimeZoneInfo.ConvertTime(gmTime,          timeZone); // 03/02/2013 8:00:00AM
  var localTimeConverted        = TimeZoneInfo.ConvertTime(localTime,       timeZone); // 03/02/2013 
  var unspecifiedTimeConverted  = TimeZoneInfo.ConvertTime(unspecifiedTime, timeZone);
  Console.WriteLine("Converting GMT         to EST: {0}", gmTimeConverted);
  Console.WriteLine("Converting Local       to EST: {0}", localTimeConverted);
  Console.WriteLine("Converting Unspecified to EST: {0}", unspecifiedTimeConverted);
Results in:
Local time zone is 'Pacific Standard Time'.
Converting GMT         to EST: 3/1/2013 8:00:00 PM
Converting Local       to EST: 3/2/2013 4:00:00 AM
Converting Unspecified to EST: 3/2/2013 4:00:00 AM
Or if your local timezone is 'Eastern Standard Time' you get these results
Local time zone is 'Eastern Standard Time'.
Converting GMT         to EST: 3/1/2013 8:00:00 PM
Converting Local       to EST: 3/2/2013 1:00:00 AM
Converting Unspecified to EST: 3/2/2013 1:00:00 AM
If you'd like TimeZoneInfo to treat 'Unspecified' like Utc, you should function like TimeZoneInfo.ConvertTimeFromUtc. Again from MSDN documentation
DateTimeKind.Local, Throws an ArgumentException.
DateTimeKind.Unspecified or DateTimeKind.Utc, Converts from Coordinated Universal Time (UTC).