OK, so you lost it a bit pitchwise when it got up high, and you have no breath control or understanding of when to breathe and when not to, and how to phrase well, but you've got a voice and you knew when to sing and when not to sing and your rhythm was pretty OK. Plenty of people hereabouts, me included, who don't start from that strong a base. And shit, I'm available on iTunes. Who'd have thunk it?
So yeah, pursue it if you want to - just make sure you've got something decent/better to sing - Hallelujah is such a cliche. You're not quite Jeff Buckley.
There's plenty of people who'll tell you you've got a good voice - that's what friends do - but if you don't know, and you lack the confidence to pursue it on your own, then go to a teacher and learn some skills. They'll tell you you've got a good voice too, that's what you're paying them for and if they don't, then you won't come back, will you? But you'll learn. Work out what you can do, and what you can do with what you can do.
There's many a great singer who can't sing for shit, technically. It's not their singing, it's what they're singing that matters.
You want to just do a better version of Hallelujah? Don't bother. You have something interesting to sing, or want to find something interesting? Go for it.