XPCOMGlueLoad error for file /path/to/thunderbird/libxul.so:
libdbus-glib-1.so.2: cannot open shared object file: No such file or directory
Couldn't load XPCOM.
Above you can see the exact error. My first instinct was to do a web search, but that didn't bring up anything useful. However, reading the error made the problem obvious: libdbus-glib-1.so.2 could not be found! I run Debian unstable on that machine, and the package that provides the file was deprecated. Anyway, easy enough to fix:
apt-get install libdbus-glib-1-2
echo libdbus-glib-1-2 hold | dpkg --set-selections