Fastest Method of Copying data from one external HD to PC?

If it won't show up on other computers, that could just mean that it won't mount, so it could just be that the file system is completely trashed. If there is physical damage, however, you're toast. If the motor spins up, and it doesn't knock the pins down in the process, I'd use testdisk. In terms of interface, eSATA would be fastest. eSATA enclosures and connection adapters are available on Newegg.com