You can put the condition after the WHEN clause, like so:
SELECT
CASE
WHEN PAT_ENT.SCR_DT is not null and PAT_ENTRY.ELIGIBILITY is null THEN 'Favor'
WHEN PAT_ENT.SCR_DT is not null and PAT_ENTRY.EL = 'No' THEN 'Error'
WHEN PAT_ENTRY.EL = 'Yes' and ISNULL(DS.DES, 'OFF') = 'OFF' THEN 'Active'
WHEN DS.DES = 'N' THEN 'Early Term'
WHEN DS.DES = 'Y' THEN 'Complete'
END
FROM
....
Of course, the argument could be made that complex rules like this belong in your business logic layer, not in a stored procedure in the database...