Both the restore (which failed) and the syncing music require accessing and transferring much larger amounts of data than the other syncing tasks.

Sounds like you have a USB problem, most likely faulty USB drivers, or potentially USB hardware (which generally would require a motherboard replacement).

It could also be something else wrong with your computer hardware wise (internal HD failing, faulty motherboard, or bad RAM)

Try copying your music to an external disk and then try to sync your music from the other computer that worked for restore. This will rule out an intermittent fault with the iPhone and also any problems with the USB cable.

If that works, then you should be taking a closer look at your computer, do you have problems copying large amounts of data to other USB disks or devices? Do you have other unexplained crashes?