Having an iCloud account won't affect syncing between a device and a computer's iTunes, iCloud just allows you to back up a device's content (documents, files etc, not the contents of the Music app) and to potentially keep Safari bookmarks, contacts, calendars in-line between the two.
Is that the computer that the iPod is normally synced to ? When you select music to sync you are effectively saying replace the music that is on the device with the music that you've selected to sync. If you don't have all of your music in that computer's iTunes library then you should be able to copy iTunes purchased music back from it via File > Devices > Transfer Purchases. For music from other sources there are some programs listed half-way down this page which should be able to copy it back : Recover your iTunes library from your iPod or iOS device.
Or if you want to copy content to the iPod from multiple computers then manually manage your content instead of syncing : Managing content manually on iPhone, iPad, and iPod
When manually managing content, you can add content from multiple libraries to your iPod or iPad. Even when manually managing music, some content may be available from only one library at time. This includes all content on iPhone and video content on iPod and iPad.
