Logging in users can see the content. It's ROLE #1 (anonymous) that can't see the nodes EVENTHOUGH, and I repeat, the permissions are set
I've seen this before - it tends to mean your node_access table has gotten corrupted. There should be a single entry (at least) in there for user 0 (the anonymous user). If there's nothing in there, then that's your problem. How much control do you have over your database? Can you get access to it to manually run commands?