Estate Law Questions? Ask an Estate Lawyer.
Please accept my condolences for the passing of your father.
Unfortunately what you describe is very common in cases of elder abuse (financial elder abuse), where individuals such as caretakers and other fiduciaries get an elderly person to agree to transfer control or ownership of their assets to others.
Unfortunately to deal with this problem you really need to hire your own attorney (and the earlier you do so the more likely your odds of recovering these assets). Look for a trusts and estates, or a probate attorney, with experience in litigation and elder abuse.
You can find local attorneys using the State and local Bar Association directories, or private directories such as www.AVVO.com; www.FindLaw.com; or www.Martindale.com (I personally find www.AVVO.com to be the most user friendly).
If a person dies without a will, their assets will pass through "intestate succession" (see: http://www.nolo.com/legal-encyclopedia/intestate-succession-new-york.html)
The New York Courts have some very basic information on how to deal with probate matters, here: https://www.nycourts.gov/courts/nyc/surrogates/faqs.shtml, but based only on what you have posted, I am willing to speculate that you have a very complex matter that you are going to have to deal with (secreting your father and his assets away, refusing to notify you of his condition, or his assets, refusing to notify you of his death, etc. etc. are all strong indications that there is potential fraud or elder financial abuse which has occurred).
I cannot tell you for certain that this is the case, but I would encourage you to at least meet with a local attorney to discuss your matter. Your local bar association is your best resource for referrals.
Those kinds of wills (leaving everything to the caretaker) can usually be challenged as being signed with "undue influence" but again, you are going to want to speak to an attorney about this, it isn't something you can easily do on your own.
If you do insist on doing it yourself, plan on spending a lot of time in the local law library, look specifically for probate law practice guides (books used by attorneys to help with strategy tips, commonly used legal authorities, and templates for commonly used moving papers).