It really depends on how important the data is to them. Bank stuff, photos, business statements send it off. If it's their bookmarks or something give it a try. It will cost them up to several thousand dollars for the professionals, depends what it is worth to them.
Also I had a drive that refused to show in the bios on two machines, but my usb/ide connector saw it perfectly! Saved my ass for sure.
You could try getdataback, recovermyfiles, photorec and testdisk, chkdsk, hdd regenerator, spinrite, ontrack professional, etc.
Is the partition screwed up? Bad filesystem? Drive making noise? Do a google search, there is a wealth of info out there.
Again, you need to talk to the client and have them SIGN something about their data. Prioritize what they want and get that first if the drive is iffy, and then get the less important stuff.