В Archwiki есть много полезной информации.
Dropbox: Known Issues.
Ваш случай похож на эту проблему:
Dropbox does not start — «This is usually because of a permission error»
Errors caused by running out of space
A common error that might happen is that there is no more available space on your /tmp and /var partitions. If this happens, Dropbox will crash on startup with the following error in its log:
Exception: Not a valid FileCache file
A detailed story of such an occurrence can be found in the
forums. Make sure there is enough space available before launching Dropbox.