That is a good momma.
I know it sounds bad, but I actually use a needle to open them. You do it very, very carefully and scrape instead of poke. You scrape away the calcium and then pry up a small piece of shell. You can then look inside without poking into any veins or the chick, as the air pocket is large enough to prevent this.
However, if you think the egg is rotten watch out, as they STINK when you open them. They sometimes even explode (we had this happen... not fun).
If a chick is nearing hatching it should respond if you cheep to the egg. Hold it up to your ear and listen for the tapping of a beak or the chick cheeping. If it doesn't respond, it may have died trying to hatch.
Its hard to know how long to wait because you don't know when the egg was laid. However, if you do know when it was laid then waiting until day 23-24 is about right.
We were sure this egg was dead but opened it up carefully from the top (the white part is the membrane stretched around him). He was still alive! Precious grew up to be strong and healthy.