I don't know if my current campaign is a good reference. The gods themselves have been largely absent and/or unavailable for direct query or interaction, but clerics still have spells and the churches still have power.
One point about a D&D style holy man: I tend to see them as dyed in the wool religious fanatics. That is, they aren't running on blind faith, or even inspired faith. They know for a fact that their deity exists. They pray to him/her and their prayers are answered every day when the god or goddess fills them with divine power, renewing their daily spells.
So while they will acknowledge the existence of other deities, particularly within the same pantheon, they will brook absolutely no deviation in the worship of their deity. The rules are clear, the deity has spoken at least once (probably in person) to make their wishes known. The higher level clerics can actually talk to the god via Commune, Divination, or even Contact Higher Plane if anything ever needs to be clarified. Angels, in the form of Archons, Planetars and even Solars, can be called in via the various Summon spells, to give direct testimony about what's going on. There really isn't any room for doubt or debate, which I see as the hallmark of a religious fanatic.
Now in our world, divination spells that call for answers from the higher powers directly are failing. Anything bigger than an Augry just flat fail. There is no deity available to pick up the phone and give out advice. But Healing spells work, protection spells work, other divinations work. The gods still exist, that is certain.
The world you're talking about is more of an agnostic world, where the deities are cut off or have abandoned it for lack of believers.
Just for fun, take a look at the Terry Pratchet book, Small Gods. It deals with a god who decides to manifest in the mortal world, only to discover that although he has a great and powerful church with lots of followers, they believe in and follow the church, not the god. In fact, he discovers, he has only one person in the entire theocratic empire that actually believes in him.
The book is light and entertainings, as most of Pratchet's works are, and includes a few scenes with the philosophical skeptics who argue that there really aren't any gods. Note that they tend to do this while inside building with well grounded metal roofs, to keep the lightning of those non-existent gods from killing them for their heresy.
Over all, though, it might give you another view of how a world like yours came to be.