First off I might recommend a detour into this recent question. Even though the problem is analogous to yours I think some of the core elements are important. After all, you can only lead a horse to water.
As far as the religious immersion, I had a DM who used only the Greek deities for all characters - none of the standard ones associated with D&D as it was her world. Every character no matter what level of piety they possessed had a deity assigned to them if they didn't choose one. Characters would feel uncomfortable if in the realm of an opposite deity and the converse was true as well - peripheral deities (and we had some of the more obscure ones than the standard Dodekatheon and thus needed to compare) led to feeling comfort in some appropriate fashion.
When it comes to the setting itself, your biggest help is what visual aids come into the game. A lot of players - especially the more experienced ones - already have an idea of what a game of D&D should entail no matter how you describe your setting verbally. Have tokens, insignias, flash cards for important NPCs, and structure the way things are accomplished. The "video game" experience can make players only think of the abstract actions that it requires to obtain something: Give shopkeep money. Approach NPC, get info. Attack monster, get XP. So if you give them more to it than "John-ius wants to see a gladiator fight" the flavor isn't just different color frosting on the same cake.
