Due to a broken pipe in the kitchen, in February, we had to have our engineered hardwood floor replaced. It took several months of quotes, etc from the insurance company and the work was finally started a few weeks ago. It took 2 days to get the original floor out (due to the glue used 9 years ago). It took another full day and 1/2 to put down the new floor (also engineered hardwood). It's been 2 weeks since this was done and my wife and I notice that when we step on certain areas there seems to be a "squeaking sound" coming up. If we stand on the area putting all our weight on it, then it stops.
I would like to know if this is natural?

Not natural and unacceptable. I would call back the installer an demand he fix the problem. Squeaks happen when wood rubs wood or a nail. This could be your sub floor or the new floor,I can't tell from here.

There is a concrete base floor and a cork sub floor was put on top of that. The hardwood was then glued to the cork. So there are no nails. Hope this clarify what I might have left out.

That is the sound of the glue breaking contact. Either there was a dip in the floor, the product wasn't installed firmly enough, not enough adhesive, wrong adhesive, etc. It could be the wood pulling from the cork or the cork pulling from the slab. Tough call. Any chance that when they removed the damaged floor that they took moisture readings of the slab? Probably not if they pulled it one day and installed the next. Unfortunately with the slab, cork, and engineered wood, and the adhesive manufacturer, along with the flooring installer, there will be a lot of finger pointing. Your best bet would be to get an inspection from each vendor prior to having the installer back into your house.

Thanks everybody, I guess the best thing is my wife or myself to stand on the floor and press it down(? ) as this seems to help. If it continues to get worse we do have a two year warranty on the product which we will take advantage of and request they come back and fix this situation.

The longer you wait the less likely that repair will be adequately covered by the warranty. Does that warranty actually state that installation errors are covered, usually not since the warranty usually comes from the manufacturer and not the installer. I'd start making noise now.

In the next few days my wife and I will be putting a letter together, outlining a few things we would like the installers to come and look at. We have a two year warranty guaranteeing that the floor has been completed to our satisfaction.