Worse, starting calibre on the netbook could have created an empty metadata.db file, which would then be sync'ed back to the other devices, possibly emptying your library.
Use calibre to check your library on your main machine. If it looks OK, then run the db check function in advanced tab of the GUI preferences. After that, check that metadata.db doesn't have conflicts (file name will have both 'metadata' and 'conflict' in it). If such a file does exist, then you might need to go to the dropbox website to select the correct version from the list of previous versions it maintains.
Don't start calibre on any of the client machines until the downloading is finished everywhere. Then be sure to start it on only one machine at a time.
Good luck!