I was a candidate at the annual election for Board of Directors and the sitting Board Broke State Law

The lawsuit should seek a court order (a.k.a. "injunctive relief") to run a new election that complies with state law and the bylaws.

You or your lawyer should first threaten this, through a series of demand letters that gradually escalate the tone, explaining that the HOA risks significant HOA attorney fees and an increase in its insurance premiums.

If I execute a proxy stating I vote for Walter, does that proxy satisfy the quorum requirement to hold the meeting or did I have to also execute a proxy to a person in attendance at the meeting so the quorum is met. I believe the latter is true.

If the election was done by mail, meaning that they sent out ballots to everyone, then proxies would not have been utilized.

If the election was done at a meeting, meaning ballots were handed out at the meeting, then proxies should have been utilized.

My first question would be would your proxies have allowed the Association to reach quorum?
If not, that election is not worth the fight and focus on future elections.
If they would have, then you have to consider is the fight worth it.

You asked what would are the possible outcomes:

1) A judge sides with you and orders a new election.

2) A judge sides with the Association and nothing changes.

What you also need to ask is what are the unintended consequences?

For Outcomes 1 or 2:
a) The membership may become divided
b) Expecting the Board would put a claim in to the D&O insurance - possible increased premiums.

Specific to Outcome 1:
a) Cost of holding a new election (printing, postage, room rental, etc.)
b) If you still don't reach quorum - nothing changes

Specific to Outcome 2:
a) Board or Insurance attorney may, through the courts, request reimbursement of reasonable attorney fees.

Perhaps I should have clarified.

If ballots were mailed out, a meeting wasn't required.
You still had to have enough ballots for a quorum, but proxies would not be needed because voting was done by mail.

Per: 14-3-707. Action by written ballot.
(a) Unless prohibited or limited by the articles or bylaws, any action that may be taken at any annual, regular, or special meeting of members may be taken without a meeting if the corporation delivers a ballot in writing or by electronic transmission to every member entitled to vote on the matter.
(b) A ballot in writing or by electronic transmission shall:
(1) Set forth each proposed action;
(2) Provide an opportunity to vote for, or withhold a vote for, each candidate for election as a director, if any; and
(3) Provide an opportunity to vote for or against each other proposed action.
(c) Approval by ballot in writing or by electronic transmission pursuant to this Code section shall be valid only when the number of votes cast by ballot equals or exceeds the quorum required to be present at a meeting authorizing the action, and the number of approvals equals or exceeds the number of votes that would be required to approve the matter at a meeting at which the total number of votes cast was the same as the number of votes cast by ballot.
(d) All solicitations for votes by ballot in writing or by electronic transmission shall:
(1) Indicate the number of responses needed to meet the quorum requirements;
(2) State the percentage of approvals necessary to approve each matter other than election of directors; and
(3) Specify the time by which a ballot must be received by the corporation in order to be counted.
(e) Except as otherwise provided in the articles or bylaws, a ballot in writing or by electronic transmission may not be revoked.

If the ballots were not mailed out, then a meeting is required and the vote would have taken place at the meeting.
In this case, proxies would be allowed.

14-3-724. Proxies.
(a) Unless the articles or bylaws prohibit or limit proxy voting, a member may vote in person or by proxy.