The Internet host is not above the law. You have a contract issue and contract law would apply. I have not seen the contract with your host (also known as their Terms of Service,) but I can tell you that when I write a TOS I put in a clause which says the host can "cancel your account for any reason, or for no reason.) I suspect the host has the same clause. If that is the case, the host is not in violation of your contract.
You can use the links to your old site to create a new site at a new host. You should read the TOS of the new hosting site to make sure what you are doing conforms to their TOS.
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We lawyers on Avvo are not a computer tech support service. But if you want a new set of Terms & Conditions or other contract, some of the best in the business are here on Avvo.
I am not your lawyer and you are not my client. Free advice here is without recourse and any reliance thereupon is at your sole risk. This is done without compensation as a free public service. I am licensed in IL, MO, TX and I am a Reg. Pat. Atty. so advice in any other jurisdiction is strictly general advice and should be confirmed with an attorney licensed in that jurisdiction.