The clicking noise is the read-write head trying (and failing) to free itself from the data platter. The two should never come in to contact so it's definitely a failed drive and no PC will ever be able to detect it, much less read the data on it.
The only way to get data off a failed hard drive is to send it to a data recovery service who dis-assemble it and access the platters with special equipment as used in crime forensics. But that will cost you, big time.
And if the head has crashed into the platters, much of data will be damaged and lost anyway.
Clicking can also be a symptom of a bad controller board. It is possible to switch controllers on the drive (assuming this is an IDE/SATA) drive; however it has recently become more difficult to do it. Find an identical drive, remove the controller, you will need to swap firmware chips from the bad board to the good one which will require some good soldiering skills. You can then put the good controller onto the bad drive. I have seen this fix the "click of death" issue before, but it is by no means a guarantee. If this is truly critical data, contact a professional service.