I have a QO6-100RB Service Panel. I was planning on adding another circuit so I turned off the 100 amp main breaker on the outside of the building (it is in a six gang meter pack). I then added the second circuit and attempted to turn the power back on by flipping the breaker in the meter pack.

It will not switch on. I push the breaker into the on position, but it will not stay there and returns to the off position. I then removed all the breakers inside the service panel and tried it again. Still doesn't work. Now I can not get any power to the service panel.

The grounding wire inside the service panel from the SE wire originally was going to a grounding bar that was added after the service panel was installed. I moved the grounding wires to the neutral bar thinking that may solve it (as shown in the picture) but it is still not working. The only thing I can think of is that the wire is grounding out somewhere, but the wires, panel and service pack are all under 2 years old and the 5 other meters are working great so I don't know what the problem is.

When you say the breaker returns to the off position... does it latch on and trip, or does it latch at all? Sounds like you have a bad breaker. Is there a sound relating to it returning, or just won't stay in place? And what is that ground wire doing there? It almost looks like you have the ground on one of the hot busses. Put things back the way they were. If you have no load, and no short you have a defective breaker. With the breaker off, you can check the wiring with a multimeter. And where is the grounding bar?

The ground bar is in the lower left, obscured. The ground wire belongs there, not where its at.

Ground and neutral must remain isolated at sub-panels.

I moved the grounding wires to the neutral bar thinking that may solve it (as shown in the picture) but it is still not working. This quote prompts me to strongly suggest you get an electrician to check this out and to do this job for you.
In fact it is most likely required. Where is it that you have a six-pack meter? If it is commercial or multi-family dwelling it is almost guaranteed that you cannot legally do this electrical work there.

The breaker does not latch at all. I just push it into the on position and it does not latch and then returns to the off position. Sounds like it's the breaker, then. I will put it back the ground wires back on the grounding bar and have an electrician replace the breaker.

Please tell me my eyes are lying to me, or does the picture really show a grounding conductor crossing over the buss?

K.I.S.S. is correct, the grounding conductor should be connected to the grounding buss in the lower left hand corner. Because it is fed from a meter stack, this is a sub-panel. The only place the grounding and grounded (neutral) conductors should be connected is at the main service panel.

If the breaker does not reset, either there is a fault, or the breaker is bad. An electrician can determine if the problem is in the breaker or the wires.

If the breaker is bad, keep in mind the line side will be hot unless the meter is removed from the base. It is illegal and dangerous for the property owner to remove the meter from the base. The service conductors are considered "unprotected" by the NEC. (The utility follows a different code, and is allowed to fuse the conductors at a higher ampacity than the NEC allows.)

Because of the amount of power available at the service, many utilities now require their metermen to wear arc flash rated clothing, face shields, and voltage rated gloves to install and remove meters, and the utility may also fine you for breaking the meter seal. There are also fines for working without a license and permit. I agree with Stan. You need to call a real electrician for this job.