Windows 7 on Bootcamp doesn't want to boot. Can't copy files from Bootcamp to Osx mavericks
Since the problem followed the hard drive when connected to a new computer, you have a clear case where the problem is disk based. The slowness, the error, and that it seems to be getting worse would make me think that you may only have a short amount of time to finish your recovery efforts.

Worst case, the drive itself is failing and you can only get files off while it cooperates. Best case, the file system is corrupt and once you zero the drive entirely, it will work properly. The test that determines which of the two is the case involves erasing the entire drive, so plan for the worst and hope for the best. 


Consider stopping your recovery attempts if the data is of value such that you would pay a professional. If it is hardware, time may run out and running the drive could make things worse. 
Prioritize and get the most important files off that drive entirely considering both the Mac side and the Windows side. 
Use PC file recovery tools on the Boot Camp side, use Mac recovery tools like Data Rescue 3 on the Mac side. Also, don't overlook tools like rsync that can ignore errors and keep trying to copy other files after running into the initial error - 36. 


Good luck. It seems like you have a good handle on various options for getting files off the drive so I wanted to offer some other options. Also, you made no mention of backups whatsoever - depending on how recent your last windows backup and last Mac backup are, you could reduce the scope of your efforts accordingly.