You might want to try doing a system restore if the hard boot got it to pair, but there is still static. If after that there is still a problem, then I would take it to a store (Apple preferably) and see if you can pair there to another phone and if the static problem still persists. If it does, then it's the headset and you should resturn it for another one.
If it doesn't then it's a strong possibility that your iPhone needs repair.
If it doesn't then it's a strong possibility that your iPhone needs repair.