Use old Macbook as NAS/Fileserver?
You can use the USB drive plugged into the busted computer as a network drive with OS X's file sharing.

Mount the drive with USB. Go to System Preferences-> Sharing -> File Sharing. Turn it on and click the plus button. Click on your USB drive and click Add. Add your user account on the right.

Now, go to another computer on the network. The busted MacBook should appear in the Finder sidebar. Click it and click Connect As. Type in your username and password (the one you use on the busted MacBook). Let it log in. Click on the USB drive and let it load the list of files. You should now see your USB drive mounted on your desktop.

Now, to configuring Time Machine.
By default, TM doesn't let you use a network drive unless its a Time Capsule. But, you can allow it do so by changing a hidden preference.
Open Terminal (/Applications/Utilities). Type this in and press enter:
defaults write com.apple.systempreferences TMShowUnsupportedNetworkVolumes 1
Now, open System Preferences -> Time Machine. Turn it on and set it to use your network drive.
Backups will be slowish, but they should work.

If you want to use iTunes and Time Machine, you'll need to use Disk Utility to partition the drive into two partitions. Time Machine needs a whole partition to run...

If you do that, just make sure that you select both partitions on the busted MacBook's Sharing System Preferences pane. Set up Time Machine to use one partition, and add your iTunes folder on the other one.

Notes: The MacBook will have to be turned on for you to get at its files.
320GB is kinda small for a Time Machine disk, especially if you're partitioning to keep media on it. Just be careful...

Hope this helps.