I understand you want to set up Apple Pay on your new Mac, which is a perfectly fine thing to do, but after entering all your information and clicking Accept and continue it does nothing. Is that correct?
It's not supposed to be this difficult. Apple really, really wants you to be able to use Apple Pay so that you can buy stuff with an absolute minimum of inconvenience. Since your Mac is new, you should avail yourself of Apple's complimentary 90 day phone or chat support. Start here: Official Apple Support.