One of the most common mistakes with data recovery scenarios is attempting to recover the data without knowing EXACTLY why the hard drive stopped working.
Correctly diagnosing the problem is the FIRST step. Most of the time advanced recovery technology is required, as well as experience.
Simply saying my "Hard Drive is Dead" is not going to tell anyone what is needed to get the data off. Most of the time failed hard drives need to be repaired, unless it's problems that cannot be repaired like: bad sectors, damaged platters.
Never the less if it's a drive that is not spinning up there are quite a few reasons: stuck heads, spindle, motor; bad circuit board.
If it's "dead" in other ways it could be: bad firmware, too many bad sectors, corrupt file system, damaged or weak heads, crashed drive.
In any of these situations as long as that platter is spinning the condition is going to get worse without fixing it first, or having the right equipment to get around the problem.