Welcome to Psych Central. It is troubling to have sexual problems in a relationship and the natural response often is to try something else physical. That is not always the problem.

From what you say your gf grew up in a repressive and possibly abusive environment that could have contributed to a low sense of self esteem and to a physical reaction of shame and guilt when any sexual feelings are experienced. Some kind of psychological damage could have been done then prevents her not only from experiencing orgasm, but also being trusting and physical. Therapy regarding abuse can help with these conditions.

If you want to approach things from a physical standpoint, be next to each other for a half hour forgetting about sex, just be with each other. Establish emotional intimacy. Don't try to do sex. Just be satisfied with that. Then the next time start out with a half hour of being together, hugging and holding and being together, plus some touching or a back rub. Eventually she may feel enough trust to get more sexually intimate, but she is not being willful IMO, she appears to be triggered or set off by sex.

Here is an article that might be helpful to you both.
https://www.google.com/url?q=http://...snXioC-2Gwg3Bg