Unfortunately, a hard disk drive (HDD) is a powered device. To extract files from a HDD, it needs to have not only power, but a system which allows the HDD to interact with its' environment (operating system, file indexing, data bus, I/O channels etc.).
This means that to extract files from a HDD, the drive needs to be powered, and connected to a computer which is also powered.
Having a hard drive attached to an unpowered computer effectively stops communication between the hard drive and the computer trying to access the files.
I am unaware of any HDD's which are operable without system power.
Compare the situation with having a CD player, an amplifier, and a set of speakers. If the amplifier is turned off, the sound from the CD player will never get to the speakers.
In order for the one computer to access the HDD in the other computer across a network, both machines need to be powered, turned on, and booted.
An option might be to purchase an external drive or storage device. There are many options, personally I would go for a USB device, as they are "hot swappable" ie. you can connect or disconnect the drive without having to shut down, connect/disconnect, reboot to access the drive. A conventional hard drive would do the trick, or alternatively, there are many storage devices available which plug straight into the USB port, and can handle anything up to (maybe higher than) 1GB of data. They are about the size of a short, thick pen, or a couple of batteries, and will connect to any computer with a USB port and the required software installed.
Hope this helps...