For a commercial software that may help you out I recommend SpinRite. It's a little expensive ($89.00) but it does the job well. If you can not get any free utilities to get it to work I would try it as a last resort. It will read the sector as much as it can then mark the sector bad. When it tries the "read as much as it can" its not just doing a normal read, it actually reading the raw data off of the head and doing probability statistics to figure out what is supposed to be there. Be prepared to wait a while, it will continue to try until it has exhausted all possible ways to read the disk, I have heard people have let it run for months as it cranks away at a bad sector (and get the data back).
A lot of people knock SpinRite for recovering the data in place instead of copying the data to another drive, but you must understand that SplinRite is not for restoring data like other data recovery tools. It is a tool to allow other tools like HD Clone and DD to work.
Followup to other question in original post:
Does this sound like something a replacement circuit board might fix
or is it probably a mechanical issue?
No the issue is on the drive platter itself, replacing the circuit board will not fix it. If it was the circuit board the drive would not read at all, not go to a specific sector and stop.