Your contract should ideally not just cover how often invoices should be made, but also how and when payment by your client should be made and late fees. The late fee part is there to protect you from this exact scenario. Your contract says you should be paid every two weeks. If your client violates this agreement beyond a reasonable timeframe, that's on them.
You've noted that the company has a document that explains that contractors are typically paid after a month, but that's a detail that should have been worked out when they signed a contract with you. Follow your contract in this instance.
So your client's decided not to respond to you. This happens, but it's important to realize that it's possible your client looked at your e-mail and simply forgot. Assuming good intent to begin with is a good idea to maintain a friendly business relationship. So, that said, send them another reminder, potentially highlighting that you have a late fee agreement they signed that will need to be paid after a given time has passed since your invoice notice.
If your client decides to continue to ignore you after a few reminders across a couple of days, it's a sign that things might start to turn legal. Ensure you're documenting all of the work you've done up to this point, and all communication between you and the client. This is to strengthen your case should you need to take them to small claims court. Contact the client across other platforms, whether that's in the form of a phone call, texting, various social media... You need to get them to respond somehow. Don't be afraid to be annoying at this point. As a freelancer, having to resort to legal matters is not ideal as it can seriously cut into the time you have available to spend on other projects and can carry a decent cost.
If a sizable amount of time has passed since the client has ignored your first invoice and your frequent other attempts to contact them, it's unfortunately time to talk to a lawyer. This isn't ideal, as suing your client should be the last resort, but it's unfortunately necessary at the stage where you're being ignored this heavily.
Talk to your lawyer (you should ideally have one you can get legal advice from) and provide them with all of the documentation you've collected. Ask them to contact your client for you. Speaking from experience, it's a bit comical how quickly you can get results once the one contacting your client is a lawyer on your behalf. If that attempt at contact doesn't work, hopefully your lawyer will now how best to move forward with a lawsuit. How well your case fares from here is up to your legal counsel.