Grapefruit -- propagate by planting fruit?

My neighbor has a wonderful old grapefruit tree with large juicy fruit and tons of seeds. The kinds in the stores don't have seeds, but they also don't have this wonderful old fashioned flavor that I remember from my childhood! I'd like to start my own tree, and I have a whole fruit from last season (January) and am wondering --if I plant the whole fruit, could I get a tree or two? I've tried starting with just the seeds, and nothing happens.

I live in central Florida so conditions are great for grapefruit! Need help. . . someone new is moving into the neighbor's house, and I'm afraid they will chop down this wonderful tree!

Thanks for any help!!!