Well if the one system is down how do you plan to transfer? Its not like connecting the 2nd PC you would be able to scroll thru the files like a webstie and take what you want. You would have to have some sort of OS running on that PC to do something like that over a network. Not having an OS is going to hurt you in every way. So if taking the drive out then try using a Linux Live CD to get something running then hook them up via a router. Cant do it thru USB. Only other way is by direct connect ethernet cable. Make sure you can transfer PC to PC. It not like the ethernet cables that you would use for the internet. Some of the wires in there are crossed to transfer PC to PC.
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Phone: LG Optimus G Pro
Running: Stock JB from LG with Nova Launcher