DNA has nothing whatsoever to do with fertility.
Fertility tests start with simple blood tests that show whether her hormones are right.
After that is a HSG test - where dye is injected into the womb, tubes and so on so any abnormalities can be easily seen on an x-ray.
Then perhaps a hysterectopy is carried out - a tiny camera inserted into the womb so the doctor can have a good look.
A post - coital test is a smear test carried out at the time of ovulation and shortly after intercourse. This shows how compatible her partner's sperm is with her cervical mucous.
A biopsy may be done of the womb lining shortly before the period is due to start - a simple scrape. This shows if the womb is capable of supporting a fertlised egg.
So you can see it is not easy to determine why a woman is not getting pregnant, and there are a whole lot of tests to be carried out which can take a long time.