The Emperor's body is physically about as dead as you can get, but he is such a powerful Psyker (read: magic user) that they keep his body alive on life support in order to harness the powers of his brain. The life support system (Called the Golden Throne) is so demanding that they literally need to provide him ~1000 human sacrifices per day, specifically people with psionic/Psyker capabilities.

However, a huge amount of the Empire's logistical infrastructure depends on him, since his mind provides a beacon (called the astronomicon) that allows ships to navigate the Warp (another dimension, full of Eldritch horrors, useful for FTL travel, similar to D&D's astral plane).

Most of the empire has become convinced that the Emperor himself is a living God, that he is omniscient and can enact his will around the galaxy. They are somewhat justified in this as well, since praising the Emperor is an effective way of repelling demons (IIRC this is just because believing in anything with enough zeal will repel demons).

Also, as soon as someone begins to doubt the divinity of the emperor, the chaos gods are able to start influencing/corrupting them, so it's generally considered a dick move not to praise the emperor. Agnosticism, atheism, and even just having your own interpretation about the imperial cult literally represent a threat in the same way a terrorist might.

The canon keeps it pretty ambiguous whether or not he’s actually alive IIRC. Several of the alien races refer to him as a “corpse emperor”, and obviously human sources in-world are unreliable. Either way, since he hasn’t actually been seen for 10,000 years, the effect is the same as OP describes.

As I understand it - Basically it's assumed he is kept barely alive to keep the astronomicon (the beacon for warp travel) working. Some people think he is a perpetual (someone who can revive after death) but if he leaves the throne the warp in Terra won't be kept in check anymore and will be lost. Most likely they'd lose the ability to travel the warp as well.

When you put one existing thing in your game, it's stealing. When you mix two existing things together and put the resulting mixture in your game, it's called being creative.

Don’t be discouraged! As a player, the only thing better than an entirely new fantasy concept is one that I’m familiar enough with to recognize and role play my spin on it! I’m sure your players will enjoy spotting the similarities and a appreciate whatever you do.