Sorry, this is not a US immigration law question.
PROFESSOR OF IMMIGRATION LAW for over 10 years -- This blog posting is offered for informational purposes only. It does not constitute an attorney-client relationship. Also, keep in mind that this is an INTERNET BLOG. You should not rely on anything you read here to make decisions which impact on your life. Meet with an attorney, via Skype, or in person, to obtain competent personal and professional guidance.
Yes. The OFAC and EAR regulations are very broad and are applicable to US citizens, foreign nationals, and essentially any American interests domestically and globally.
There is a good chance that the Syrian address is at the heart of the issue. You should consider, too, when OFAC regulations with respect to Syria sanctions were first put into place. It may be that the company was required by the OFAC regs to cancel your account, which, perhaps were not in place when you first opened the account. Still, if you have lost valuable data (not merely personally, but data on which you can put a "dollar value", it may be worthwhile to hire counsel to get an opinion on what rights and remedies may be available to assist you.
You should hire an attorney to contact the web hosting company and explain the problem. At the very least, they should be able to get them to allow you to retrieve your data.
You may want to discuss your situation with a lawyer in more detail. Most lawyers on Avvo, including myself, offer a free phone consultation.
This post is provided for general informational purposes only and is not intended to be legal advice specific to you. This general information is not a substitute for the advice of an attorney in your jurisdiction. The attorney client relationship is not established by this post.