Do you happen to be friends with a cheerleading coach or a former cheerleader? I'm not sure how she did it exactly, but a friend of mine potty trained my son in one day (he was 2 1/2)...she did the same for friend's child and her own son was using the potty by 20 months (and fully trained by 24 months).
I started in June (a few years ago now) when I got out of school for the summer...put him in underwear and resolved not to go back to diapers during the day (except when we had to go out somewhere)...a month later I was tired of cleaning up the messes. He would sit on the potty when asked but never did anything in it. I was considering going back to pull-ups when we decided to have a multi-family garage sale at my house. My cheerleading friend was there all day and she offered to take over taking my son to the potty every time he showed signs of needing to go. The first couple of times, still nothing...but she was very upbeat and would do a cheer for him when he tried. Then, that afternoon, she got him all excited and took him to the potty and he actually used it for the first time (#1)...the cheers she did got him so excited he was bouncing all over the place...and an hour later, he did #2 in the potty too.
From that day forward, my son used the potty on his own!...we had maybe three or four accidents after that but by the time he started pre-school in mid-August, he was fully potty trained...even at night!
Like I said, I have no idea why it works for her...at first I thought it was largely because she is such a pretty girl and the little boys (my own and the other one) wanted to please her (i.e., that unlike their mommies, the boys didn't feel the need to assert their will over her)...but it worked for her son too. I keep telling her that she should rent herself out as a "potty-tutor".
Good luck...they all train eventually...try to make it as fun and exciting as possible and you might see some positive outcomes faster than using punishment.