First principles:
1) It is not possible to make a hard drive fail simply by doing a Finder copy.
2) They are seven kinds of irresponsible for having a central data drive with no backup
This is like removing all of the nuts from the company car's wheels, telling the newbie to drive to the post office, and then blaming him for the wheels falling off.
Every hard drive in the world will fail, sooner or later. It's a given.
Now:
Go and get a new external hard drive, or better, a new external case and a new mechanism, so you can easily swap drives in and out
NOTE: If you don't have an internal hard drive in a Mac that has enough free space to back up the dead drive, best get 2 new, large drives.
Make sure that the enclosure is of the correct internal connector type for the dead drive -- most usually this will be an IDE drive.
If you can borrow or buy DiskWarrior software, that may come in handy.
You problem may be software (the logical structure of the info on the drive), it may be the case/bridgeboard/power supply of the external case, or it may be the hard drive mechanism itself.
You want to install the mechanism into the new enclosure (this removes the variables of the enclosure, power supply and cabling), AND have another drive ready to backup the first one as soon as you can fire it up. Act on the presumption that if you can get the drive to appear, it may be the one and only time it will work before failing completely.
Once you are set up and ready, you can try going into Disk Utility, and see if it can recognize the drive (even if the Mac volume is not recognized) If you can, do a Repair Disk on it.
If you can't see the mechanism, or if Repair Disk doesn't work, you can try
DiskWarrior. DW does not repair hardware problems, but it does a very good job in repairing a certain class of logical errors in the catalog and volume data of the drive, and often can make a 'disappeared' drive reappear.
Back up the data to a second drive the moment you gain access to it.
If DW can't make the drive visible then you have more serious problems. A program called
DataRescue may be able to scavenge data from the drive.
If that doesn't work, you need to start considering a professional data recovery service such as ActionFront, DriveSavers, Total Recall or Seagate Data Recovery. This will cost thousands of dollars, typically.
There are other, riskier things that can be done to attempt to access the drive, but you don't want to risk destroying the chance of recovery at one of the professional services. Generally, the more you **** around with it, the lower the chance of eventual recovery.
Whatever the outcome, I suggest that the company hire in a consultant who can assess the network and the data, and install a proper, automated, redundant backup system with archiving and offsite storage. This may cost 1 or 2 thousand dollars, but the balance of that is "What's the cost if all your data disappears?". How much money would be lost if all the work and records had to be recreated?