I think you've dug yourself so deep a whole that you're chances of having any sort of relationship, friendship or otherwise is pretty much zero.
She no doubt thinks you are a creep and potiential stalker and her only solice is that her Brother is your room mate which probably makes her feel safe to a certain extent. Buying gifts for people is all well and good, but for people you only know in passing eg;She's my Room mate's sister, I see her time to time but at your own admission haven't had a conversation 1 on 1 means you don't know her. Buying her a Birthday card would be seen as sweet. Buying her a trinket at a kiosk down town might be seen as generous. Buying her a $3k ring would be seen as Stalker/Creepy/Crazy.
Basically most Women I know see Jewelry as something you buy for Mom, Sisters, Grandma, Godparents and your Girl. Outside of that it is crossing a boundry that you've stomped all over. Which is I think the heart of the issue is that you have come very close to crossing the line, and offering her the gift would be crossing it.
Seeing as this has been going on for a while, I would summize that she has played the scenario out in her head already and either thinks you're a bit weird or all out crazy. She might even take the ring if you offer it but then pawn or sell it off for a quick pay day. Or she may do what's right and refuse the gift and tell you to leave her alone.
As for ever getting to see her again, I'm sure she will. After all, her Brother is your room mate and while one can avoid a confrontation no doubt you will see each other rarely and I promise it will be very awkward and I doubt it will be one on one unless you manage to get her alone only to explain or apologize for this mistake.
As for what to do with the ring. You have Two options. Return or Pawn it to get money back or you can Keep it. However keep it to give it to someone else when you meet the Woman you want to marry. This is what Diamond rings are for, engagement, not "Hi I think you're special" sorts of gifts. If you have a Girl you want to date and you start to date her then buying her earings, or a necklace would be appropreate but not a diamond ring until you're ready for the commitment of her being your Wife and you being her Husband.
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"A real leader faces the music, even if he doesn't like the tune." - unknown quote
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