Surely the Wiki "How do I become root" instructions are horribly out of date now? The easiest option these days is to install becomeroot (or some equivalent package that modifies the gainroot script).

And dropbear is an anachronism and nothing but a pain in the arse, it doesn't automatically start (as the OP has discovered) and comes in two parts which is confusing for some users (as the OP has discovered). Dropbear should forever more be replaced by openssh (apt-get install ssh) which is simple, reliable, standardised and offers more functionality than dropbear.