Under normal circumstances, your printer working is not dependent on your internet working.
This is what it would look like.
[router] <---- [printer]
As you can see, the printer is reliant on the router working. If you lost your printer when the DSL went down, I would suspect your problem was actually your router failing, not your modem or DSL provider.
Edited by Senlis, 12 November 2009 - 09:47 AM.