registry refers to a nonexistent JRE

Sounds like the same issue that has occurred the past few Java updates.
I’m not a technical expert on these things, but there seems to be an issue with the automatic Java updater not removing all older Java references, so you need to do it manually.
Manually delete Java through the Control Panel, go to the Java website, download and install the latest version and it should solve the problem.
Let us know if this worked.