From what context?
From the context of a related table, the count function can count the number of related records where the field is not empty.
To count all records where a field is not empty for a found set of records, use a summary field defined as the "count of" this field.
I've tried using a summary field with "count of", however, that adds together the values of that field, where as I want a count of the total number of fields with a value in them, not the actal value itself.
The "count of" summary field does not sum the values. It counts those that are not empty. The "total of" summary field sums the values like you describe. Better double check the details of your set up.