Thanks for the replies. So it's not just me then.
Well, it seems to have cured itself, as usual. Though, I was almost at the point of taking it in for service. I tried everything I could think of, and then it occurred to me that if I put the computer to sleep and then wake it up, the ROM drive will usually make a zip-zip noise (the head repositioning, I assume). So, I put it through the sleep-wake cycle a couple of times, and was then finally able to put the disk in. Seems to be working for now anyway.