What were the terms of the contract? Most software development contracts state that the rights to the deliverables are transferred client upon full payment. If that is the case, then you still own the content. You could just remove the work you performed until payment is received.
However, this will most likely cause more harm than good in terms of negotiations, unless the work you did was mission critical.
Regarding claims court, a judge would look at the fact that you completed work for a client. If the client has not paid you at all for your work, then the court will most likely look at the fact that you performed a service for nothing. When contracts are ambiguous, courts use a reasonable person standard whereby one could argue that it was unlikely that a provider would perform services for no consideration.
If you received partial payment, then it becomes tougher because the client could argue that you didn't perform the work to the full letter of the contract. Some contracts state that the completion of the project is at the discretion of the client. If this is ambiguous, again the reasonable person standard applies, but it's much harder to measure in that case.
In short, if you defile the client's website, you may never get your money, you may lose the reference, and the possibility for more work.
Honestly, it hasn't even been 30 days! Most clients expect a 30 to 60 day grace period when working with a vendor. Remember, you're not an employee, you are a porfessional contractor, a business entity.
I would recommend you take a deep breath, and wait and see what happens. The client is human too and just got through the holidays. If you wait this out you may discover that you get payment as well as more work! If the delay becomes extreme, like past 60 or 90 days, then take action.
My credit card company isn't even this itchy to get a hold of my money :)
DISCLAIMER: I am not an attorney. I have studied some business law, but I do not consider myself an expert or professional in this area. I have not passed the bar. I worked for a contractor for 2 years building software and received payment every 60 days. My contract was clearly spelled out, and neither myself nor my client had any disputes.