DNS will never have anything whatsoever to do with your physical connection as Steve said. But if your DSL is hosed you certainly can't reach a DNS via it.
With multiple DNS entries, if the first one is available (but hosed), the others might not be attempted. A dead DNS is better than a sick one
.
Try using 8.8.8.8 or 9.9.9.9 as the first DNS in the list to test in this situation, but I would only do that as a test, not as a permanent change.
Oh yeah... get thee a smart phone (with data) as a backup for DSL outages if it's chronic. How else are ya gonna ask PPOT for help
?