welcome to HeathcareMagic
No playing of badminton in no way will affect or disturb in getting pregnant.The problem you may be having for not getting pregnant is PCOS
which is a condition which can lead to anovulatory cycles;irregular periods
.So please consult your Gynaecologist and get treated for the PCOS and she will give the treatment for induction of ovulation so that you can get pregnant soon.
All the best.