You're getting a lot of shit answers. Don't shut down the site. If you shot it down, then they pay, then they sue you for damages for lost income while it was shut down, what is your argument to a judge? Their argument is they always intended to pay, they upheld their side of the bargain, and you recklessly damaged their business. Your argument will be, "I listened to idiots on Reddit".

Uphold your side of the agreement, do everything in your power to force them to uphold theirs. That means, emails, letters, phone calls, whatever, just keep asking every week or two about the money you're owed. If you have to sue them, sue them. If you still get nothing then you can send letters stating you'll have to shut down the site without payment in 30 days or whatever. Then, and only then, should you shut down their site.

How you get them to pay is usually just, you politely pester them forever until you're certain they'll never pay, then you sue them. There's no secret to get scumbags not to be scumbags.