I called a locksmith to come take a look at it as well. I have two keys and he even cut me a new one. He replaced the chip in the keys and re programmed them. He told me that something in the lock cylinder could be broken, but couldn't give me an exact answer. He put the keys in the ignition and kept knocking it with a screwdriver...every 1 out of 20 times of pulling the key in and out the dinging stopped and the keyless entry would work. Now it just continuously beeps when the key is out.

Would replacing the lock cylinder make a difference?

I'm also not sure if the keys are charging since I am using the key with a new battery from the locksmith.