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The root cause of your problem is that you are summing from row 2 which does not contain valid numerical data. While most of the SUM functions will automatically convert non-numeric values to 0, the + addition operator does not. As a result, the expression H2:H100+I2:I100 evaluates to a 99 element array and the first value in the array is an error value. Error values are not automatically converted to 0. Consequently, the entire expression evaluates to an error.
The simplest solution is to change the starting row of each array expression to row 3. The following formula produced the intended results.
=SUMPRODUCT((H$3:H$100 + I$3:I$100) * (TEXT(G$3:G$100, "mmmm") = A$32) * (DAY(G$3:G$100) >= 1) * (DAY(G$3:G$100) <= 7))
By adding the $ to the cell references, I was able to copy this formula from B34 down to B37 and change only the starting and ending DAY values for the other three rows. B37 evaluated to -268,119.09 as expected.
You can also copy these four rows to B43:B46 and change only the TEXT value from A$32 to A$41 in each. B44 evaluates to 1,019,706.86.