New Table Aggregating Column

Issue is being caused by an empty string in Parent ID.

Try

SummaryTable = 
ADDCOLUMNS (
    CALCULATETABLE (
        DISTINCT( OriginalTable[Parent ID] ),
        NOT OriginalTable[Parent ID] = ""
    ),
    "Cost", CALCULATE ( SUM(OriginalTable[Cost] ) )
)

BLANK function (DAX) - DAX | Microsoft Docs states
Some DAX functions treat blank cells somewhat differently from Microsoft Excel. Blanks and empty strings ("") are not always equivalent, but some operations may treat them as such.

To use more than one column use SUMMARIZE instead.

SummaryTable = 
ADDCOLUMNS (
    CALCULATETABLE (
        SUMMARIZE(
            OriginalTable,  
            OriginalTable[Parent ID],
            OriginalTable[Column 2]
        ),
        NOT OriginalTable[Parent ID] == ""
    ),
    "Cost", CALCULATE ( SUM(OriginalTable[Cost] ) )
)

I'm actually confused as to why NOT ISBLANK( OriginalTable[Parent ID] ) doesn't work! Can't find any reference as to when BLANK() == "" and when it doesn't.