I want a formula to write in the cell (D1) that calculate number of Days from a Day written in a cell (B1) till today as long as the cell (C1) is blank and once the cell (C1) contain a Date the value showed in the original cell (D1) is the number of Days between the two cells (C1) and (B1)
Assuming the dates are not text, something along the lines of
=DAYS(B1,IF(ISBLANK(C1),TODAY(),C1))
Not as robust, as the solution by @robleyd but showing/using the implementation of dates, being stored itself as a number of days since beginning of 20th century:
=IF(C1=""; TODAY()-B1; C1-B1)