Glad you were able to sort it out - iPod cables and USB ports can sometimes by mysterious in their variability - though in your case the symptoms suggest that a conductor may have failed inside the cable you were using. I've found that, using a selection of cables:
- my 2G nano will occasionally be detected as being connected via USB 1.0 (even when connected to 2.0 ports)
- my 3G nano syncs fine but steadfastly refuses to charge when connected to any of the USB ports on my main computer, though using the same cable charges happily when connected to a USB AC adapter
Such things are just sent to annoy us 😉
On your other question, it is possible to completely replicate your library across two or more PCs. As long as the iTunes database (iTunes Library.itl) is duplicated as well as all your media you then have two physical copies of one logical library, with which iDevices will sync on either computer. See turingtest2's notes on Make a split library portable to see how to verify that your library is in a consistent structure to make replication easier, and Backup your iTunes for Windows library with SyncToy on one method for replication (typically using an external hard drive that also serves as a regular backup). My configuration looks like this:

where the library on my "master" system is replicated, using MS SyncToy and an external HDD, to two other systems - a secondary one at home and one in my office at work. My iDevices will sync to any of these without the "threat" of wiping their content because iTunes detects that they've been previously synced to a different library - because of the replication method used the "unique" library identifier that iTunes uses in the sync process is actually the same on all three systems.