Is it possible to prove the existence of a god...

Is it possible to prove the existence of a god, or another being not residing in the same dimension as us, with only evidence from this world?

Great question! Here's my take. Christians do believe in another "dimension", or realm, or whatever you want to call it. This realm is the "supernatural." Not in an eerie, ghost-like way. But simply "above nature." It is the realm of the divine, of ideas, morality, will and intelligence.

Your question of evidence is directly on point. As another response to your question observes; there are an infinite number of things to believe in, if you require no evidence. The evidence for this realm is within ourselves.

If you look at yourself, you can observe that you have a free will. You can choose to do, and not to do, a wide variety of things. If there is nothing above nature, from whence does this remarkable ability come? If we are nothing more than atoms and space, we should be nothing more than a ball rolling downhill. Our trajectory, speed and ultimate destination determined as soon as we began to move, determined by the physical laws that control all other matter. Yet we aren't that way. Even people who hold that they have no free will, don't behave that way in their real lives. Just take off with their wallet and see how quickly they believe in your free will and hold you accountable for it. ;->

We also observe that we have morality. That's a word that carries a of baggage these days... I'm talking about large scale morality. Like, it's better to feed a million people than to torture them to death. However, morality itself depends upon a supernatural realm. If there is not a "good" defined and enforced by something higher than nature, then there is no "good" at all. And there is no "evil." If this is the case, than there really is no ultimate difference between Mother Theresa and Hitler. There's no difference between giving your kid a hug or pushing him down the stairs. Again, even people who deny the supernatural, don't really live their lives that way. If you try to do something evil to them, they (either themselves or through law enforcement) hold you accountable for what you do. They expect you to know the moral law and respect it, even while denying that there is a moral law.

There are more examples, but this is already getting really long. The point is this. There's something special about humans. We are matter, but we are free. We are animals, but we recognize morality. If there is nothing above nature, than those are illusions. And if they are illusions, than "humanity" is an illusion. We may as well murder, steal, rape and plunder, because it doesn't make any difference, and we're not in control anyway. But if you look at yourself, I believe that you know better. You don't know in a scientific manner. Science (the study of nature) is powerless to study that which is above nature. You know internally. You know in what a Christian calls "your heart." It's a part of you. And you'd have to work to suppress it.

And that's, IMHO, is the answer to your question. The evidence of God is in you. In your will. In your morality. The one place in all of creation where you have the "inside track." We don't know what it's like to be anything else but ourselves. And when we look at ourselves, we find evidence for the supernatural... or if we don't, we find what C.S. Lewis called the "Abolition of Man" if we deny the supernatural. For we have to deny all that makes us human.

Speaking of Lewis, he's was a former atheist, just like me. And a professor at Oxford, totally unlike me. :) He's also the guy that wrote "The Chronicles of Narnia." Anyway... If you're interested more in this topic, I recommend Mere Christianity. It's a good rundown on "generic Christianity" for the thinking man. Read that and you'll see what Christianity really is, rather than the stereotypes.

The Holy Grail is not an object

I strongly disagree. I mean no offense, but I'd guess that you're trolling. But, on the off chance that you're serious... you're building speculation on top of supposition on top of speculation.

This is most likely a mistake, or a misunderstanding due to faulty translation of the original text.
What evidence do you have that this is "most likely?" And what "text" are you referring too? The term "holy grail" does not appear in Scripture. The earliest mention of anything resembling "the holy grail" is in Helinandus' Gradale around 720 A.D. Most "grail" legend is from a relatively small period in the middle ages (1180 and 1240). So any "text" you're referring too is going to be very far removed from the events in question.

Since there is ample evidence to suggest Jesus was in fact the descendant of Solomon and David, and therefore he was true Royalty
This is true.

Which is exactly why they killed him (jews did not), if he was even killed, which is not even certain and cannot be proven.
This is not true. Pilate went out of his to try to set Jesus free. Fearing a riot, he finally acquiesced and had Jesus killed. As far as Jesus' death being "not even certain and cannot be proven," what standard of proof are you looking for? You seem ready to believe, and spread, all sorts of speculation on the flimsiest of evidence. Yet you're unwilling to accept the death of Christ, which is one of the most heavily documented events in the history of the world.

So if Royal Blood is indeed the proper translation of sangraal, and due to its inherent connection with Christianity then it most likely refers to Jesus' bloodline.
Again... the proper translation of what? You're constructing a house of cards...

As is generally believed, Mary Magdalen moved to the South of France after the crucifixion...
Actually, almost no one believes this. There is an 11th century legend of Mary Magdalen going to France, but it is utterly without foundation in fact. Most likely, Mary Magdalen retired to Ephesus with the Blessed Virgin as stated by St. Gregory of Tours.

There is also ample suggestion in the gospels of Jesus being married...
Now you're just getting strange. There's no evidence what-so-ever of this in the Gospels.

It is in fact a lie concocted by religious leaders trying to obfuscate the fact Jesus was a married man with a family; being married and having children was practically required at that time and it's unfathomable that he didn't.
Again, just plain wrong. You only have to look at the writings of St. Paul:

Now to the unmarried and the widows I say: It is good for them to stay unmarried, as I am. But if they cannot control themselves, they should marry, for it is better to marry than to burn with passion. (1 Cor. 7:7-9)

But if you do marry, you have not sinned; and if a virgin marries, she has not sinned. But those who marry will face many troubles in this life, and I want to spare you this.(1 Cor. 7:28)

I would like you to be free from concern. An unmarried man is concerned about the Lord's affairs--how he can please the Lord. But a married man is concerned about the affairs of this world--how he can please his wife-- and his interests are divided. An unmarried woman or virgin is concerned about the Lord's affairs: Her aim is to be devoted to the Lord in both body and spirit. But a married woman is concerned about the affairs of this world--how she can please her husband. I am saying this for your own good, not to restrict you, but that you may live in a right way in undivided devotion to the Lord. (1 Cor. 7:32-33)

The fact is that the Last Supper was a Passover meal. At a Passover meal there are four cups of wine consumed. Jesus lead the meal and had a cup which he shared. If the cup still exists, it's location is unknown. The legend of "the holy grail" is a product of middle age fiction. The "history" you're trying to build around it baseless.

Oh, and in case you were still wondering, I am an Atheist.
I used to be an athiest... or at least an agnostic. Here's a book by another former athiest that I recommend. Many people, especially on slashdot, gravely misunderstand Christianity. This is a book for intelligent people interested in what Chrisitianity really is... not what it is sterotyped to be.

Notably, you can download the MP3s for the complete album of me playing my piano compositions:

• Geometric Visions

I expect to make Ogg Vorbis format available soon as well.