PC to iPod.
During the sync process, iTunes will copy tracks from the PC to the iPod, adding tracks or removing tracks according to the state of the playlist or the library (if syncing all)
Tracks that are NOT in the library will be removed from the iPod while tracks that are added to the library will be added to the iPod.

You need to remove the iTunes library, and your media, from the dead machine and transfer it to your new machine. This is probably not a wise move considering the reason for its demise.

There are a number of utilities that will allow you to move tracks from the iPod to the PC, Google for them, or you can try this way:
Connect the iPod to your PC. If a sync starts, hit the X at the top right of the window to close iTunes.
Go to Control Panel, Portable Media Devices and double-click your iPod.
From the Tools menu, choose Options, then the View Tab
Check "Show hidden files and folders."
Navigate to the Music folder.
Dig around here for the music.
Select all the music folders, and drag them into a folder on your Desktop. You can even drag them into itunes directly.

Once done, launch iTunes and in the preferences set iTunes to Organize you Music.

Hope that helps