How can I count unique values in one column based on criteria in two other columns?

I am trying to to count the number of unique entries in column A where Column C says NO and column D says YES. However, I cannot devise a formula to do this based on two different criteria. How could I do something like this?

For instance, I want to know the number of unique countries that have viewed an event on-demand but not live, which would be 4 in the following example:

country  |  Preview  |  Live  |  On Demand
GB       |  NO       |  NO    |  YES
GB       |  NO       |  YES   |  YES
ES       |  NO       |  YES   |  YES
DE       |  NO       |  NO    |  YES
FR       |  NO       |  NO    |  YES
US       |  NO       |  NO    |  YES

From the formulas suggested in the answer below I have managed to get excel to accept the following formula but this does not return a value. The aim of this is to enter a 1 in column F if E is equal to 1. Any help would be appreciated:

=IF(E=1, IF(FREQUENCY(MATCH(A2:A214, A2:A214, 0), MATCH(A2:A214, A2:A214, 0)) > 0, 1, 0))

Would you consider adding a formula that simply comonbines values of both columns, and another that counts new/unique values?

Formula for E =$C:$C&$D:$D

Formula for F =IF(COUNTIF(E$1:E2,E2)=1,1,0) ( this is example fopr cell( F2)

country  |  Preview  |  Live  |  On Demand | Combined | New/unique
GB       |  NO       |  NO    |  YES       | NOYES    | 1
GB       |  NO       |  YES   |  YES       | YESYES   | 1
ES       |  NO       |  YES   |  YES       | YESYES   | 0
DE       |  NO       |  NO    |  YES       | NOYES    | 0
FR       |  NO       |  NO    |  YES       | NOYES    | 0
US       |  NO       |  NO    |  YES       | NOYES    | 0

You can use the following array formula to get the count of unique records meeting all criteria. Paste the following into the formula bar and press Ctrl+Shift+Enter.

=SUMPRODUCT((C2:C8="NO")*(D2:D8="YES")/IF(COUNTIFS(A2:A8,A2:A8,C2:C8,"NO",D2:D8,"YES")=0,1,COUNTIFS(A2:A8,A2:A8&"",C2:C8,"NO",D2:D8,"YES")))

It's long and a little repetitive, but it should work for you. This formula uses the 1/COUNTIF(...) trick that's shown up many times on this site in the past for counting unique records. I had to introduce the repetitive IF condition to keep from getting #DIV/0! errors.

What the formula does:

SUMPRODUCT with one array argument just adds the elements of the array. The multiplication terms go to 0 if either condition is not met, and 1 if they are both met. The division by the COUNTIFS is a way of scaling this value to get the unique count. For instance, if there were two records for GB with On Demand but not Live, each of those records would get scaled down to count as 1/2 of a record in the total sum. If there were three such records, each would count as 1/3. That way when the sum adds these records, the total sum for GB On Demand but not Live will be 1, e.g. 1/2+1/2=1. This is how uniqueness is captured.