Count A Cell If Criteria Is True In Another Cell

I have been looking through about 4 pages of these threads and searching the internet and can't seem to find my answer.

I am trying to count about 400 cells in column N if a different criteria is true in column M. The numbers in row N are a dollar amount, and the criteria in column M is the type of donor. I need to know how many donors there are of each type. The trick is that there are two other columns with dollar amounts for each donor, and I am also counting based on what event donors made gifts for.

Column M - Donor Type (designed by a letter "E", "A", or "P")
Column N - Annual Appeal (dollar amount by each donor)
Column O - Off-cycle (dollar amount by each donor)
Column P - Event (dollar amount by each donor)

I have a summary chart at the top of all this that should be able to tell me how many donors of type E donated for the Annual Appeal, how many donors of type E donated for the Off-Cycle, and how many donors of type E donated for the Event, etc based on donor type.

I've tried COUNTIF using multiple criteria, SUMPRODUCT, all kinds of things. Usually what happens is a get a #VALUE returned or the function counts the total number of donors by type (ie 269 E donors when what I want to know is how many of those donors donated to the Annual Appeal).