Just because there is no pelvic pain does not mean the fallopian tubes are open. Fallopian tube diseases and blockage are among the top three reasons for infertility.
Sometimes this may be caused by endometriosis, a condition where the inside lining of the uterus is on the outside of the uterus. Some women do have symptoms of endometriosis, such as pelvic pain during the menstrual period.
But in general, a blockage of the fallopian tubes does not produce any symptoms. You need to have the patency (openness) of the tubes tested with a hysterosalpingogram or laparoscopy if you want to know whether they are open or not.