If you have issues to connect your Slingbox to the network, I suggest you the documentation below, please follow all of the steps.
Thanks, I had already tried all of those steps before posting here.
I've actually done some more hunting through the forums since then and have found that the common theme seems to be faulty PSU. I managed to find another 5V PSU and my Slingbox has burst back into life. I've now ordered a proper replacement.