This feels like a strain in the translation. In order to make it work in my mind, I have to process it further:
He was deterred by the thought that [there was] not one of his sufferings [except that it] was common to all the others ...
That's still rather a precious and poorly put together statement in modern English, but at least now it has a bit more glue holding it together. In plainer words, it means
There existed not a single one of his sufferings that was not like all the others.
and, even plainer:
All his problems were more or less the same.
This relies on the use of but meaning except that:
4. With the exception that; except that. Often used with that: would have joined the band but he couldn't spare the time; would have resisted but that they lacked courage.