Wa'alaikum salaam Amir. . .
I dont think that the reason the girl's parents dislike you is because you are white - the reason they are against this entire issue is because Dating is not considered a lawful activity in Islam. . .
You could have been Chinese, Black, an Arab etc, if her family has Islamic values - they would still have disliked you. No muslim parent wants to see thier child dating.
Marriage would be the only option - however, before you take any such steps, you should give yourself time to dwell over the issue, and not make any emotional step. After all, marriage is a serious commitment. . . and are you sure this is love, and not a romantic fantasy you both have built around urselves?
Perhaps the elders DO have a backward notion of not marrying outside race/clan etc. But that is trivial - a marriage cannot/should not be prevented based on this alone.
I urge you to remain steadfast on your faith, and continue praying. However, I would also sincerely urge you to stop Dating . . . there is no such thing in Islam - and unlicensed romantic-contact b/w unmarried persons is wrong. (even if it be nonsexual)
Think about the issue a bit more, and if you still want to marry her - approach the Parents politely by stating that accord to Islam, there is no harm in inter-racial marriages, and what matters is that u both follow islam and are happy etc. . .
From a cultural perspective: Approach the Father, and make your honorable intentions known to him, tell him u will take good care of her etc, declarations of undying love are not required, just a polite, practical conversation. Tell him that you will be sending a formal proposal - have your parents meet them, etc and bring your family into the details. In the sub-continent, the Girl's Parents lay a lot of importance on the family, and are wary of marrying thier daughter off when they have limited info/details about the family background. . .bcz they do not know how serious/honorable u are. Also - many consider it unsuitable for a young man/woman to pursue a suitor on thier own, rather prefer families to do it for them - that apparently reflects on the 'modesty' of the person. Nothing Islamic abt it, just cultural . . . Islamically nothing wrong with u proposing urself.
"O Lord, forgive me, my parents and Muslims in the Hereafter. O Lord, show mercy on them as they showed mercy to me when I was young."