Timing of new queen created from a split?

[Algonam]

Langstoff hives. Deep supers. 1 year old. Carnolean breed. Beekeepers since Spring 2011.

On June 6th we decided that it was time to try our first split. We had a double brood chamber that was very strong and with queen cells as well. We pulled 3 frames of mixed honey/brood/pollen and created a nuc which we moved to another location many miles away. We have inspected both the nuc and the original hive twice since and have seen a reasonably good volume of bees but no sign of queen activity in either so we figured we killed the queen by mistake in the process.
We took a peek at the original hive yesterday and still didn't see any new brood. Just lots of honey production. If we killed the queen, each half of the split would have to produce their own queen cells and the process continues from there.
Now it is just over 1 month later (after splitting) and we are wondering how long it would normally take from a split like that to start to see some new brood? We want to leave them alone but don't know if we should take another peek in 1 week or 2 weeks.
All info is appreciated.

[FRAMEshift]

Are there queen cells in either/both hive?  If the bees made queen cells, the virgins should have emerged 16 days later.  After that, it takes time to mature the ovaries, take mating flights, and get the hang of laying eggs.  You could be seeing eggs/larvae by now, or it could take another week or two.  But if there were no queen cells made, both hives are in trouble now.

I'd take a close look to see if there are remnants of opened queen cells in each hive. What you want to see is at least one cell that is neatly opened at the bottom, indicating that a virgin queen emerged.

[Algonam]

Yes, remnents of queen cells are there, but every time I inspect I risk squishing the queen. Hope I didn't squish a new queen since she emerged. The frames are all gunged up with comb and honey and there seems to be alot of squishing going on when removing and re-installing the frames. This is why I want to stay away for another week or 2 before inspecting again.
I guess only time will tell ?

(I can't figure out how all of the hive inspection videos I see don't have anywhere near as much comb and honey and excess build up that I have...the stuff that makes it very hard to pull a frame. Sometimes it requires alot of strength to pull a frame because the lower frame wants to come up along with it and everything gets shifted around)