It's likely that any browser that runs on Snow Leopard (10.6.8) will be unable to access most https Web sites.
After people discovered that the original method used to secure https connections against eavesdropping was not as secure as previously thought, there was a movement to replace it on Web sites and in browsers. I believe (could be mistaken) that the first version of Safari to get the update was in one of the releases of El Capitan.
P.S. - According to MacTracker, a "MacBook 3,1" would be a MacBook (13-inch, Late 2007). You can upgrade that Mac as far as Lion, and no further. It is unlikely that Lion will have any more luck with the Web than Snow Leopard will.