I have a Western Digital 2TB Green Drive (WD20EARS). I came home one day after leaving my computer on (I leave it on 24/7) and the motherboard was fried (literally had burned parts). I got a new board & power supply as everything else seemed fine. A few weeks later one of my hard drives started freezing up on transfers of large files. It seems like it's getting worse the longer it's plugged in. I booted into safe mode once after unplugging all but this drive and the os drive and was able to copy almost everything off. There's still about half the drive that I have not recovered, and can only copy small files off at a time. Any suggestions for larger transfers? Everytime I boot up the os now warns me that my disk is failing and I should back up. It does a chkdsk everytime also.
Have you checked the cabling? Are you using new one, or the one from the old motherboard? I would replace the cabling outright and try again. Also, worth trying a different port, different OS (Linux, etc) and different power connector.
When a motherboard crashes there is a 70% chance that hard drive can generate bad sectors and because of which it is freezing like you said and because of that only you are not able to copy large files. My personal suggestion to you is to use a data recovery software. These days recovery tools are really cheap. they have a way to skip bad sectors and will help you copy your data faster. but also keep in mind that you should not let the recovery software run without supervision. wrong attempts can result is head crash and can leave scratches on platter.
On a 2TB drive depending on how much data you have but if its 50-60% full you should not take more than 5-6 hours to recover everything using a recovery software.