Is there any correlation between dilated cardiomyopathy and fibromyalgia?

Not really: Not in the true sense of the word, not that we know of anyway. However, sometimes fibromyalgia is a misdiagnosis (like in the case of lyme disease as one example), in those cases, the muscle pains and aches and the cardiomyopathy maybe part of one and the same malady.

No: None that has been described in good peer-reviewed literature. These are two separate diseases that may be devastating in their own way.