Unfortunately for you and many homeowners the harsh truth is that HOAs have power. Fighting them will cost you money. No one ever brings these abuses up to the legislature to curtail their power, and fighting them on your own is 10 times as expensive as paying up.
The property you bought came subject to the association via the Covenants on the property. You should have received a copy of the Covenants at or before closing. The Covenants spell out your responsibilities and their powers. Normally, the Covenants state that at a particular time of year the dues are fixed and payable, usually in January. Whether you get a bill or not, a notice or not, letters, phone calls or any communication at all is irrelevant according to most CCRs (Covenants, Conditions & Restrictions).
Yes, as Mack and Grace point out, you usually will get a copy by un-certified mail of what was sent by certified mail and it is your responsibility to read the notice, and the notice is considered delivered when they deposit it, not if you pick it up.
You might try communicating with them, preferably by mail, that you did not receive the prior notices, apologize for heaven's sake, for the misunderstanding and send them a check for the original amount due, at a minimum. Ask in your letter if they will please forgive the additional fees. Of course, they will most likely refuse to remove them and bill you again for the missing amount.
Pay it. On your payment check write the property address and that you are paying under protest -- something like HOA Dues 123 Elm - PAID UNDER PROTEST. This notation, when presented in a court of law, indicates that you did not willingly pay them but rather under duress. If, and this is something you need to discuss with an attorney, you decide to sue them over the additional fees, it is best to show that you did pay them but under protest. You cannot sue them for a loss you had, if you didn't actually pay them. Justice of the Peace court can handle your lawsuit, but the judge will ask you to prove your loss so that he could potentially award payment to you. Refusing to pay altogether can have dire consequences.
Does the HOA have the power to foreclose? Yes. Will they? Some do. They're heartless idiots. The property is subject to liens that are superior to the HOA's lien. Taxes are always superior, period. If you have a mortgage loan, that lien is most likely superior as well, even though the CCRs were filed prior to the mortgage. The reason is that most CCRs contain a subordination clause, which basically puts the HOA's liens behind your mortgage even though filed first. Otherwise, lenders would not be disposed to offer mortgage loans on residential property.
But, the HOA must follow its own rules. The Covenants say what they must do in order to have a valid lien. The corporate By-Laws of the HOA itself also restrict how the HOA must act, and the HOA may have adopted additional regulations after the CCRs and By-Laws. These regulations, typically requiring consent of the homeowners affected, are refinements, like no swimming after 9 PM or no alcohol at the clubhouse, etc. The priority is that the CCRs must be followed by the HOA guided by the By-Laws, and lastly if not prohibited by the Covenants or By-Laws, the rules and regulations must be followed by both you and them.
The reason that the priority of liens and priority of documents is important is that if the HOA is required by the CCRs to follow a particular sequence of events to fine you or to foreclose, or if the HOA is prohibited from using agents to conduct proceedings against you, or if they must offer a hearing and did not, you have grounds to reverse the actions they took. The bad news is that you need to prevent them from foreclosing first and then sue them afterwards at great expense.
Further, most HOAs don't realize that the priority of liens means that their foreclosure does not prevent later foreclosure by taxing authorities or your mortgage company. They think they get the property free and clear. They don't. So, if they're holding title to the property and not paying the mortgage, they lose title to it. The same story with taxes. They went to all the trouble of wresting title from you and kicking you out, only to lose possession to someone else. Idiots. They take on the expense of your mortgage and taxes and insurance, if they actually foreclose.
Yes, do consult a lawyer, but you should send the HOA a nice (no nastiness) letter explaining your mistake and asking for forgiveness. (You don't want further aggravation -- just a solution.) After you have staved off the foreclosure, do what you should have done years ago and read the CCRs and By-Laws. Figure out your responsibilities and whether they followed the rules. Then try talking to the president calmly without remonstrations.