Answer: You are normal for you. Do not compare yourself to others. There are women who are not able to experience orgasm without the intense stimulation a vibrator provides. There is nothing wrong with you, that is just the way you are.
Certainly have sex with your partner, but do not try to have an orgasm every time. Learn to give each other pleasure versus orgasm. Let your partner know that they can give you pleasure with their touch. Remember, orgasm is just one form of pleasure. Your partner should forgo orgasm on occasion, as well, so you can both explore different types of pleasure.
Teach your partner how to use the vibrator, so they can use it to give you pleasure. A vibrator is a tool they can use to give you pleasure, just like their fingers or tongue.
Note: The following information about testosterone is outdated, please see the article about androgens.
If you find that your vulva and clitoris are insensitive to stimulation then consider having a doctor test your testosterone level. If it is low, they can prescribe a 1-3% testosterone cream for you to apply to your vulva daily to increase your sexual responsiveness. Another option is Viagra. This usually works best for women who once had good sexual response but do not presently because of illness or disease.
There is a new cream called Viacream that is basically a topical stimulate. I do not recommend it, mostly because they charge way too much money for it, and it is not the wonder cream they claim it is. It is an expensive scam in my opinion.
Consider introducing erotic material into your love making sessions. Perhaps watching an erotic or sexual video, looking at erotic pictures, or reading an erotic book while they manually or orally stimulate you may result in orgasm. The last thing you want to be thinking about is orgasm; if you are thinking about having one, it is much less likely to happen. Explore mutual anal stimulation and intercourse as well.
You have a means of giving yourself pleasure, do not under value that. An orgasm is an orgasm. There is no such thing as a bad orgasm. The problem has nothing to do with orgasms; the problem is with you and your partner's expectations, which are very likely unrealistic.