解析：

　　考点：句子结构的完整性(Sentence Construction);时态(Tense);用词(Wording)

　　首先， 原句主语为two Swiss psychologists，以此判断谓语动词一定出现在划线部分。declaring是非谓语结构，故不能作谓语动词。纵向比较选项，相同的错误也出现在B选项中。而CDE选项的declared可以作主句谓语动词。

　　其次，declared that 后面的宾语从句也需要主谓结构完整。C选项having failed为非谓语结构，故不能作其谓语动词;D选项的fail、E选项had failed都能作谓语动词。

　　再次，区别时态。fail是一般现在时，had failed是过去完成时。而主句动词declared表示过去的事情，故从句里是在此之前发生的动作，选had failed正确。

　　(A) declaring不能作主句主语two Swiss psychologists的谓语动词，主句缺少谓语动词。

　　(B) declaring不能作主句主语two Swiss psychologists的谓语动词，主句缺少谓语动词。such like不符合书面英语表达习惯。

　　(C) 从句having failed不能作从句主语most of the studies的谓语动词，从句缺少谓语动词。

　　(D) 从句谓语动词fail表示一般现在时，而主句动词declared表示事件发生在过去，故应选择过去的时态。such like不符合书面英语表达习惯。

　　(E) 从句谓语动词had failed准确表示出动作发生在过去，并先与declared的动作，故符合逻辑含义。举例使用such as符合书面英语表达习惯。

　　At the end of the 1930s, Duke Ellington was looking for a composer to assist him �C someone not only who could arrange music for his successful big band, but mirroring his eccentric writing style as well in order to finish the many pieces he had started but never completed.

　　(A) someone not only who could arrange music for his successful big band, but mirroring his eccentric writing style as well in order to finish

　　(B) someone who could not only arrange music for his successful big band, but also mirror his eccentric writing style in order to finish

　　(C) someone who not only could arrange music for his successful big band, but also to mirror his eccentric writing style in finishing

　　(D) that being someone who could not only arrange music for his successful big band, but mirroring his eccentric writing style for finishing

　　(E) being someone not only who could arrange music for his successful big band, but mirroring his eccentric writing style as well, finishing