OK - found the registration problem, and perhaps the problem with task sync issue as well. The last post of
this article suggests that you need to ensure the Blackberry policy service is running. Having a look at the services on the server showed that it was indeed down. Shortly after starting this the device started up.
For some reason the BB services aren't starting up properly on reboot. I started the BB service manually via the BB Manager app, however not all services seem to startup when you start the service from there.
For the sync issue, there was another service that wasn't running: Blackberry Synchronization Service. I've started that as well and now I'm seeing tasks show up in my BB from the web client. I haven't seen tasks come back the other way yet, but I assume this will take another few minutes to sync.
John