If you place the dollar sign before the letter, you will affect only the column, not the row. If you want to have it affect only a row, place the dollar before the number.
You may want to use =isblank() rather than =""
I'm also confused by your comment "no values throughout spreadsheet - just text" - text is a value.
One more hint - excel has a habit of rewriting rules - I don't know how many rules I've written only to discover that excel has changed the values in the "apply to" or formula entry fields.
If you could post an example, I'll revise the answer. Conditional formatting is very finicky.