I've been thinkin over this logical thing for sometime, and I think I may have found a problem, although I'm not sure. I hope this hasn't been addressed and I missed it.

You say:
If God does not not exist, then He might exist. (2. ~(~G)→◊(G)), and then you go on to 7. If God necessarily might exist, then He necessarily does not necessarily exist. □(◊(G))→□(~□(G))

What I see here is a sequence that claims that there is a contradiction in step 7 because it is necessary that God might exist, which would then lead to the supposed fact that necessarily does not necessarily exist. However, step 7 is not a contradiction because step 2 is true(according to the ontological argument)

Let me explain:

If it is valid to say that God might exist and therefore must exist, then you should be able to substitue □G with ◊G (and vice versa) because they have the same value of existing, in that, because God is defined as existing, there is no difference between might existing and must existing....in either case, God exists.

So, in step 7, when you say that God necessarily might exist, that shouldn't be a problem because what you are just saying is that God necessarily must exist.

So I guess what I'm saying is ◊G = □G, therefore: □(□G) = □(◊G).

Does that make sense?

Phish, it makes sense, but my current thinking is that you would be denying the antecedent if correct.

To show this, let's start with the first part of your argument, which is that God is defined as necessary in my argument.

1. G→□G (assumption)
2. G (assumption)
3. ~~G (T from 2)
4. ◊G (T from 3)
5. □G (F from 4)

If God is defined in the premise as necessary, then my argument is invalid before I really ever get started, since step 5 denies the antecedent.

For the second part of your argument, we have to pause and discuss nested modalities (e.g., it is necessary that it is necessary that...). This includes the implication that nesting implies hierarchy, which further implies an order generating that hierarchy such that, in effect, some things are more necessary than others. This is consistent with the unnested, uni-directional modality structure, which informs us that possibility is lower in the hierarchy than necessary and, in turn, necessity is similarly lower in the hierarchy than necessary necessity.

This being the case, something that is necessary that it is necessary is more necessary than something that it just necessary. God is presumed in this argument to be necessary, not necessarily necessary, and, given the nested hierarchy, we cannot conclude that God is necessarily necessary because he is necessary. The quirky thing is that necessity can never be more necessary than it already is.

We might not like that, but it seems to me that our only other option is to discard the notion of nested modalities entirely. Yet, if we do so, then we must reexamine the relationships of unnested modalities, since they would lose their meaning. A heirarchy of nested modality for necessity implies that there should be hierarchy for possibility as well, since possibility is in the same hierarchy as necessity. We can show this hierarchy as:

...□□□A→□□A→□A→◊A↔A

With that in mind, we can now turn to the second part of your argument in which you say that if God is defined as necessary, then, if God is possible, then God is necessary. So, now, we can rewrite my argument, replacing possibility with necessity.

1. G→□G (assumption)
2. G (assumption)
3. ~~G (T from 2)
4. □G (F from 3)

This is also an invalid argument for the same reason as the first above. However, to be sure, if G↔◊G then we can replace G with □G as follows.

1. □G→□□G (assumption)
2. □G (assumption)
3. ~~□G (T from 2)
4. □□G (F from 3)

Finally, we can conclude that using our conditional premise while erasing distinctions between modalities and introducing nested modalities produces an invalid argument.

Again, to prevent destruction of the modal hierarchy and, thus, modal logic itself, it seems to me that we must either reexamine the hierarchy or accept nested modalities. I see no way to discard the hierarchy without destroying the logic itself, so I conclude, at least for now, that we would be wise to accept the hierarchy.