"Continue" button in checkout not working - help!

I'm doing some test purchases on my newly completed website. Many times, the first "continue" button does not work - it switches to "loading..." when you click it but goes no further. If I wait 5 minutes and reload the page, it then will often work. Then, however, it may get stuck on a step further into the checkout process. This seems to happen completely randomly. I see dozens of topics about this in various versions of OpenCart, with no solution yet. Has anyone figured out how to fix this?