Try to have lunch with other

co-workers if it is possible; Bring some Cookies to office and offer them at late afternoon after everyone is hungry usually;Check on him and other co-workers often like: " hey, do you want me to bring a cup of coffee." etc. Try your best efforts to smooth the relationship. by doing so, you have other co-workers on your side and slowly try to melt his defense towards you too.
Even when you walk to the manager, do not say things like in your first post. Just try to emphsize that you have deadline to meet, but he is not willing to offter help as teamplayer and give a specific good examples. Do not say things like you asked him to pass a word to somebody, he said no. Be smart and try to create some situation that he is not play as teamplayer and then present it to the manager. In office, you have to play some politics sometimes if you really want to go to manager.