Update to my original post below
I have had an extremely helpful email from Jeff Robison who is VP for Customer Care and Operations at Carbonite. He has not only apologised for the problems they created and offered a refund but also made it clear that they intend to learn from this and use it to benefit future customers. In addition, he offered to help with my particular account if it was still needed. Can't ask for more than that and a big thank you to Jeff.
I have recently changed online backup provider from Carbonite to SugarSync for the simple reason that when I did need to access the files which had been saved on Carbonite they weren't available. First complaint went in well over a month ago and having been pushed from one customer support email to another I've finally been sent an email today which looks like it might actually specifically deal with my problem. Not exactly a great service in a business where reliability must surely be top priority. Thankfully old school hard drive backup rescued most content and therefore led to minor irritation rather than disaster. It's replacement SugarSync has been excellent so far and makes it extremely easy to access your files from any computer - even the iPhone. For the sake of completeness, another tool which has been drawn to my attention but which I cannot comment on one way or the other since I haven't tried it is the Cloudberry S3 Backup which works with Amazon S3 storage.