I've been working IT for 27 years. I've been learning data recovery (slowly) for about a year. This disk needs tools and experience I don't have.

Samsung SP1614C Rev. A
F/W: 100-30
E-HD11-03-2476 (B)
09-2004

Drive spins, light regular clicks, not found by system or recovery utilities.

The client has wedding and family video and photo files. Client (of course!) is financially challenged.

Suggestions please....

Nothing you can do. If it clicks continuously at startup (without DATA cable connected) , it's most probably heads.
Can also be a firmware problem (the part stored on the platters) but in the above 2 case there's nothing you can do without expensive tools AND/OR know how.

NOTE : was by a chance the drive seen / PCB changed by someone else before you saw it ?!?