From reading your posts it sounds like you had a 320GB drive attached via USB to another external 500GB drive to back it up...I'll assume this is correct. And the 500GB drive is the one that is failing.
First, make sure to try the simple stuff first like new known-good USB and power cables. Make sure the USB cables are not over 5M in length and the shorter the better.
With the 500GB drive failing you should be able to connect the 320GB drive via usb to any Windows or Mac machine assuming it's formatted to FAT32. NTFS will need to be attached to a Windows machine. As long as you did a file copy rather than a 'buffalo' backup you should be able to access all that data fine.
When attaching to Windows the 320GB USB drive should be recognized just as an external drive.
Once you have your 320GB drive working you can then work getting the data off of your 500GB drive. This is where it may get tricky with Buffalo warranty and whatever so understand that this should be done at your own risk.
If it's a single 500GB drive in the enclosure, you should be able to take it out and either connect it directly inside your PC or put it in another USB enclosure which you may need to buy/borrow. This will eliminate the enclosure from being the point of failure.
Examples of a couple;
For IDE: http://www.newegg.com/Product/Product.aspx?Item=N82E16817145656
For SATA: http://www.newegg.com/Product/Product.aspx?Item=N82E16817153066
Once you have your 500GB drive in another enclosure or connected to your PC internally you should have a better chance at getting the data off of it.
If I have read your posts wrong please straighten me out :)
Good Luck!
