Although these are discs you've used before, have you recently started a new batch (or started putting labels on the discs before using them)? The vibrating noise doesn't sound like good news, and suggests a disc imbalance which might be the cause of unreadability.
Otherwise, as you say, the early XS-32 machines did indeed have problems with disc recognition, but firmware updates were supposed to solve some of the problems and widen the disc acceptability. However there are reports of machines of a similar age as yours needing the DVD drive replaced.
If you can't pin the problems down to the discs themselves, have a look at this thread on AV forums, which may be a good starting point for assessing what's wrong with your unit (firmware or hardware).