Answer: I am sorry to hear of you and your wife's difficulties. Rest assured you are not alone.
First, do not place too much importance on vaginal intercourse. You both can have a pleasurable and rewarding sexual relationship without having intercourse. Intercourse is only one form of sexual activity and not necessarily the best or most pleasurable. If you are not having a pleasurable sexual relationship now, intercourse is not likely to change that.
Intercourse is not required for her to become pregnant; if sperm comes in contact with her vulva, conception is possible.
As I have mentioned in prior answers on the Q&A pages, the first thing you should both do is agree not to attempt intercourse again for at least six months, or until a solution is found. Neither of you should feel pressured to have intercourse. Every time you attempt intercourse and do not succeed, you cause emotional harm to the both of you. In her case, you can cause her increased physical harm if there is a medical cause or cause a medical problem to develop.
It sounds like her hymen may still be partially intact. You can determine this by inserting well-lubricated fingers into her vagina, very slowly and gently, when she is sexually aroused. Start with one finger and as her vagina relaxes and opens up, switch to two, then three. If her vagina does not relax, do not try to force your fingers in. Massage her vaginal and pelvic muscles versus just sticking your fingers in or thrusting them in and out.
Have her try doing Kegel exercises to learn to control her pelvic muscles.
If she experiences pain, locate the location of the pain. Is it her hymen, vaginal opening, or vagina that is the cause of her pain?
Check the depth of her vagina with your fingers. You should be able to touch her cervix, if you can insert your finger(s) fully. Your penis could be hitting against her cervix, limiting the depth of penetration. Try using a different sexual position, perhaps where your wife is on top.
If her hymen is the cause, it may need to be surgically removed. This is a minor surgical procedure done in a doctor's office using local anesthetic.
The glands surrounding her vaginal orifice may be infected and the cause of the pain. This condition is called "vulvar vestibulitis." Examine the area around her vaginal orifice for redness and gently press on the tissue with the flat of your fingers and see if she experiences pain or discomfort. If she does, bring this to a doctor's attention.
Can she insert her own fingers, a dildo, or another object equal in size to your penis into her vagina? If she can, there may be an emotional cause.
You should seek out a sex and marital therapist to help you, especially since this has been occurring for three years. Medical doctors usually have little to no training in human sexuality. Your relationship has probably been adversely affected in many ways by this problem. It is normal to require the help of others in this situation.
Please read through all the information on the website together, especially the Q&A, Intercourse, Virginity, Locating the Vagina, and Sexual Dissatisfaction articles.
If you could not insert your penis at all, the medical term for this is vaginismus.