I hate to say it, but you may need to reinstall again. This time, make sure you use a clean up utility to make sure that all the pieces of the installation are removed that might not be removed by the uninstall utility. The last time I looked, Oracle was recommending
CCleaner. Uninstall Java, run this tool, reboot, and then reinstall Java. This will get any spare temp files, libraries, and registry entries that the uninstaller might have left behind. The free version should be enough to do this job.
I didn't see you mention which OS you're using, so assuming Windows. From everything I've read on this, assuming the cert path error is the root of the problem, is that it is either programmatic (meaning code isn't correct for connecting) or that the version of Java is old and trying to use old certificate validation paths that may no longer exist. If it was a programming problem, I would think it would be showing up more often. That makes me inclined to think that the problem is an old cache setting that is interfering (which is what reinstalling is supposed to fix).
As a mention, I'm not entirely sure what settings and such Java or Haven uses on Windows, how they're stored (typically in registry) or what the values are.
Another possible thought: what setting is Java security at? High may let it bypass an expired certificate as long as the other parts of it are good. Might try this if it is set to "very high" (Java settings->Security tab). Might also try explicitly adding
www.havenandhearth.com, game.havenandhearth.com to the exceptions list, but loftar says this shouldn't be necessary now.
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