The real reason why the original was so successful was the fact that was, quite possibly, the first third-person adventure game, and allowed people to really feel like they're raiding tombs. That's it.
I say screw the whole story board thing and just make it a free roaming adventure game, where you hear about artifacts, collect them, sell them, and buy equipment, bigger mansions, etc. They would have to completely remake the game, changing controls, level lay out, gameplay, etc.
My recommendation is making it on the next generation systems so the franchise is reborn, and once again demonstrates the power of the system it's on.