I have to go to court for a trial regarding an H.O.A lawsuit against me. Will a public defender take my case?

Generally speaking, the concept of a public defender applies only in criminal cases, when a person's life or liberty is at stake. In those cases, the Supreme Court has held that the defendant is guaranteed the right to a lawyer, if necessary at public expense.

I am unaware of anything similar in a civil context.

Your state may offer counsel for private civil litigants or you could try your local Legal Aid Society to see if they can be of assistance.

As has been pointed out, public defenders work for the state and represent criminal defendants, they don't represent people facing civil cases where only money is at stake, but perhaps you could enlist a pro bono Legal Aid lawyer or local law student to help you if your income and case meet their restrictions.

The HOA's total claim probably includes their legal fees and penalties, as well as the dues and late fees you owe. Presumably the HOA is authorized by the CC&Rs to add these amounts to what your debt, but it's worth checking the CC&Rs to see if their justification is warranted and their math is right.

Since the bottom line is they just want to get paid and you don't owe that much, have you tried making installment payments? They don't want to spend more money on their lawyer, so maybe if you made regular payments, they wouldn't need to pursue the litigation against you.

Disclaimer: Please note that this answer does not constitute legal advice, and should not be relied on, since each state has different laws, each situation is fact specific, and it is impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue. This answer does not create an attorney-client relationship.