I did quite a bit of googling on this, but was unable to find a definitive answer. I did see several posts about matching the VPI/VCI pair, but no word on whether or not this is something that all DSL modems do.
I did see some posts about regional differences in setting up modems, but again, nothing definitive.
It seems that most local tech stores (Best Buy, etc) carry modems appropriate for the region, so it's safe to buy locally, but that doesn't help when you're shopping eBay or Froogle.
In the end, Best Buy had the same model as the one that broke, so I just purchased that one.
But it would still be nice to know the ultimate answer to the original question.