conditional formatting of cells with quarters based on date ranges in other cells

EXAMPLE FILE:
example.xlsx

I have a file with:
- 2 columns: Column 1 = start date, Column 2 = end date
- one column per quarter (Column3 = Q3 2013, Column 4= Q4 2013, etc)

I need to color cells in quarter columns grey if the quarter in a particular column falls out of the date range in Column 1 and Column 2.
For example: Col1=8/1/13, Col2=9/1/13
since the date range is in Q3, cell in Q3 column will stay white, while Q4 column will be colored grey since Q4 is outside of the specified date range.

The date range could span multiple quarters.

Please see attached example.

Any help would be greatly appreciated!

Thanks a lot, L-Drr, for your help. I am looking for more details.

I have column headers as yearly quarters (Q1, Q2, I attached the file in my question). How do I figure out in the formula if dates from other columns fall within which quarter? How do I then specify in the formula to color quarter cells that's not within the date range?

Unfortunately, the start and end dates are not going to be one whole month in chronological order, it can span several quarters, so it's not that straight forward as manually coloring.

THanks, L-Drr, for your help.How would you suggest to do it?