Try to restore it how it is. Try to restore it in DFU mode. (10 seconds power and home and continue to hold home while connected via usb) Try to restore it in recovery mode.(10 seconds power and home and continue to hold home while not connected) post your error codes if you get any.
Restore your iPod in iTunes. Click on your ipod in the left column and you should see a 'restore' button in the center of the page. Also try syncing with a different library. (maybe the songs are the source of the problem)
The headphone jack flex cable includes all the parts that you mentioned are not working, most likely what happened is this cable came unconnected from the board. You can use this guide here: iPhone 3GS Headphone Jack Replacement You only have to go to step 3, then make sure the cable directly to the right of connector 6 (one with the red 6 sticker) is attached firmly to the logic board.
Try Repairing your disk Start up in single user mode ---- Hold CMD-S on start up Let it boot - When the text stops scrolling: Mount hdd - Type in (no quotes) "mount -uav" Filesystem check - Type in (no quotes) "fsck -f" If it completes successfully you can reboot by typing "reboot" or turn off by typing "halt" or you can run fsck again if you want.