All fixed, I hope! I replaced the battery (it was down to 0.9V), and I contacted the iOptron service people. They suggested the problem was a faulty LED on the backlight diffuser. They said they could send me a new diffuser, but when I checked it out I found that only one of 3 LED's which are built in to the diffuser was faulty. I bypassed this one, and the others do the job quite happily- just a bit dimmer on one side...
Saved me $50 and a long wait for the new part to come from the US!
Kudos to iOptron: they responded very quickly!
They also said there was no need to do a firmware upgrade, which is a good thing because I use a Mac, and that is a job for a PC!
All now seems fine, so fingers crossed.
- Dean