It is unfortunate that you did not receive your PI. However, what I have witnessed here in India, same thing has happened with my couple of friends that they did not receive Performance Incentive or Variable Incentive as per company policy in the process of Separation.
Did your company paid PI for the quarter on due dates ? OR was it paid late in one shot ? Had you already resigned on the day of allotment of PI ? If your company happened to pay PI after your resignation, I am afraid you may not claim that money as per policy. If it would not have been paid deliberately on the grounds of performance, you have a reason to fight. But remember, it is worthwhile to part with your current employer on a good note and not to burn your bridges.
You might feel it discouraging but that is what I have observed. Let us see what Seniors have to say here!
With regard to your second query, please clarify issues to your new employer. On serious discussions, you can ask what specific issues your new employer has been informed by your current HR (it is easy to give general feedback). You can always clarify your side under those specific events and prove yourself right in genuine cases.
In no case, you should bad mouth or blame your HR / Superiors as it will create bad impression on your part. Just clarify it as misunderstanding etc. BUT come forward to admit your mistakes that would have happened under those circumstances. Reassure your new employer what you have learnt out of it.
Hope it helps and all the best!
With best regards,
16th November 2016 From India, Pune
16th November 2016 From Finland, Helsinki