I vote just keep it real with her as a friend. If it later developes into a relationship, cool. If not, you still have the friendship (which making a last-ditch effort to turn into a relationship could jeapordize), and can hunt around for someone else who can make you just as, if not more, happy.
Just as a back story...
There was a girl I seemingly tripped and fell over in high school. She was a friend of a friend, who thus became my friend. At one point, her senior year I believe, I asked her out. She said no, I said OK, and we moved on. We both kept the friendship side of things up and such. We both had strings of relationships post-high school. I even moved away from here for a long while. We sort of lost touch for awhile at that point.
I moved back, and joined a band. That band needed a 2nd guitarist, and she just happened to play guitar. I called her up, and asked her if she wanted to jam with us. She gave it a go and came over for practices, gigs etc. This was our only interaction, as school and work made just generally hanging out difficult.
At the time, I was in a dead-end relationship. In fact, it was at the point where we didn't exchange words for days at a time.
As time passed, about 4 months or so, the band began to die down and split at the seams. Eventually it would disban all together and call it quits.
As I quit the band, so did she. We agreed that we should go out and chill that night, since the normally alloted practice time was now free time.
I went bowling for a short while, and she showed up at the alley

. She invited me over to her place to hang out. It was busy at the lanes, and I was throwing very poorly anyway, so I said what the heck, spend some time with a friend and such.
So we get there and over the course of about 5 hours down two bottles of rum. You would think we would've been basically obliterated at that point, but I was feeling fine, and so was she. So I put my arm around her and more or less held her for an hour or so.
I, at that point, had to leave in a hurry. I was using my mother's vehicle since it was the only one available that could haul all of my gear in one trip. We said goodnight and I left.
On my way home, I was kicking myself, as I kept saying that I should've asked her out. If she said no, I could've blamed the alcohol and laughed it off

. If she said yes, then major score!
I get home and prompty fall asleep.
The next day I get up and go online to check my e-mail and TalkBass. There's an e-mail from her, that basically said she wasn't sure why I had put my arm around her, but that she liked it.
Score!
At that point, we started hanging out a lot

. A couple of weeks later, she was hosting a Halloween party, and it was that night that we formally started dating. Was also the night we shared our first kiss.
I broke up with the other girl the next day. After not talking to her for nearly three weeks.
