Hello fellow PCOS sufferer! This question is right up my street because I'm usually anovulatory, and conceived my children through charting, supplements, and lifestyle changes.
PCOS is a spectrum disorder, and not everyone will have every symptom. According to the clinical guidelines, you need to have at least two out of these three things to be diagnosed... cysts visible on ultrasound, irregular periods, and abnormal androgens. I have the first two, but not the third. Which two (or three) you have makes a difference to your cycles, your symptoms, and chances of conception.
Ovulation tests are notoriously unreliable for PCOS women, because they measure LH surges. Many PCOS women have multiple LH surges throughout their (often very long) cycles, but their body doesn't respond to the LH properly (this can be for different reasons) and they don't ovulate as a result. If you decide to chart (which I totally recommend if TTC with PCOS) then this creates a very distinctive chart, with peaks and troughs seemingly almost at random. This changes when either..
A) Your body finally responds to the LH and creates a true ovulation, which will be recorded in your chart as a sustained rise in BBT. Your cycle will then proceed as normal, resulting in a true period if fertilisation does not occur.
Or...
B) Your body, exhausted by the prolonged effort, gives up the ghost and gives you a withdrawal bleed, signalling the end of an anovulatory cycle.
In your case, I suspect you had an unproductive LH surge (possibly more than one, unless you test for LH daily and you are sure there weren't others) before finally ovulating. However, unless you are charting then there is no way of knowing when you ovulated... sorry! It could have been that your second LH surge was productive, or that could be another red herring and you could have had a later surge (two days later? Three? Four?) which was the productive one.
What does this mean for you? It means that there's no way to reliably calculate your dates from the data you have, and you'll have to go by the dates they give you on your 12 (ish) week scan. That's OK... I've found them very accurate, actually. Whilst I've had to offset my dates for PCOS (and do some head splitting maths with my charts in front of me... just when I thought I was done with Maths, at my age!), I've found they matched the 12 week scan dates exactly, in every case.
Congratulations, and good luck!