A complex problem, to be sure.
When you say your original application was "refused," does that mean all of your claims were rejected, and you abandoned the application? The problem here is that you cannot use an abandoned application to prove prior invention. 35 USC 102(g) states that the first to invent gets the patent, unless the first to invent abandons, suppresses or conceals the invention.
Here, you abandoned your application -- which, while is not the same as abandoning the invention, does imply suppression if you did not timely try and refile for a patent -- and Company A, with whom you had an NDA, filed for and received a patent. While this may be a breach of contract issue (depending on the wording of the NDA), there is nothing inherently wrong with this scenario -- you abandoned the invention, so now a second inventor can patent the same thing without running into a 102(e) issue. This may not seem fair, but it fits with the policy of patent law -- you are supposed to give something to the public -- the information in your published patent -- in return for a temporary monopoly. If you keep something a secret, the public does not gain anything from your invention, and therefore the government is not inclined to give it the same level of protection as a patent.
So, you never had an original patent to be infringed on. If you were to go to court and challenge company A's patent on invalidity grounds; you could possibly use the NDA to prove that Company A did not invent the invention, you did, and should not have been granted a patent under 35 USC 102(f). However, even if you could invalidate their patent (unlikely, very few patents ever get invalidated under 102(f)), you wouldn't be able to get a patent because the time elapsed would bar you from getting a patent under 102(b), and the patent, although invalidated, would be a prior art reference under 102(b) or 102(e). Note, however, that you cannot use the original abandoned application to prove invention -- invention requires two steps, conception and reduction to practice, and an abandoned application can only be used to prove conception. So, without some other proof of reduction to practice, you won't be able to prove an earlier invention date, and therefore invalidate their patent.
I'm not sure where you are going with the rest of the post. You never had an original patent, so there cannot be infringement. Your second patent has gone abandoned in the US (failure to pay a maintenance fee, I presume), so you have no patent rights in the US at all. Basically, you have no rights. There can be no infringement without a patent; as I noted above, even if you could get the other company's patent invalidated, it wouldn't give you a patent, and would merely move the invention into the public domain.
I hope that answers your questions. You might want to talk with a lawyer, but it doesn't seem from your post that you really have any patent rights to assert in the US.