Assuming your by-laws state that only members have the right to vote.....
Since you want to ignore the fact that the vote was invalid there is not much you can do this year. As for next year, the group needs to stick to the voting procedure to-the-letter and keep it all above-board. Although frankly, if you are not even willing to fight for open meetings this year, I am not sure there will be much of a PTO to vote for next year (the new board can change the rules anyway they want as it currently stands).
As far as not keeping minutes - that isn't right. Even board meetings need to have minutes if votes were taken that effect the organization as a whole (but not every sensitive discussion point needs to be included in those notes - only the main topics and the results of a board vote). Our PTO board is required (by our charter) to announce every vote taken at the next Regular PTO meeting (we do it as part of the minutes).
If I were you, I would get some of the "hard working members" together and force the new board into a little openness. Point out that the original vote should be considered null-and-void since non-members were allowed to vote. It will be hard to actually get that to happen, but if you use that as a bargaining chip you should get some public meetings going and some openess from the board. If they do not cooperate, well then they forced your hand and either you fold or you go for getting the vote declared null and void and push for new elections.
At the end of last year our PTO election was held at a fundraiser that was open to anyone. People voted that were not members of the PTO, we ended up with a Pres. that hard working members didn't even know, ended up with another board member that volunteered for many things last year, but never showed up to do the job! There are no open meeting held now, (new board decision) they just decide everything and let a few of us do all the work. I told the new secretary that minutes needed to done for every meeting and she told me "No, just for public meetings" Many hard workers are becoming discouraged because of all that is going on, we have lost many volunteers. I know nothing can be done about election now, (would not even dream of putting school through that) but what you guys do when it came time for next years elections?
Thanks,
eesmom