IF formula for a range almost works, except with blank cells

Apologies if the title is too vague. I will if necessary rewrite it to comply with forum rules.

I have posted this same question here: https://www.mrexcel.com/board/threads/if-formula-for-a-range-almost-works-except-with-blank-cells-win7-excel-2010.862406/#post4188823

I'm using Win7 Excel 2010. The following formula (in cell H2) works to returns today's date when the cells in the range contain text, and returns nothing when there is a mix of text and numbers:

=IF(SUMPRODUCT(ISNUMBER(C2:G2)*1)>0,"",TODAY())

In the cells in that range, I enter [same], [none], [removed], [new record], or the date information was updated. If all 5 cells contain text, H2 should show the date the data was entered; if one of them contains a date, this is not necessary. My goal is this: H2 should be blank if the range contains text or any blank cells; otherwise, it should return today's date.

The problem is this: The formula also returns today's date if there are one or more blank cells in the range. So, how to ignore blank cells?

Probably a simple thing, and I've found several examples for A blank cell but not for blank cellS. I much appreciate your help and patience. My questions, I promise, will become less ignorant with time and medication. Thanks very much.