FULL PRODUCT VERSION :
Easier said than done - redirecting the output to a file doesn't work (presumably another bug).
java version "1.7.0_75
Java SE Runtime Environment (build 1.7.0_75-B13)
Java Hotspot Client VM (build 24.75-b04, mixed mode, sharing)

ADDITIONAL OS VERSION INFORMATION :
Windows XP SP3

A DESCRIPTION OF THE PROBLEM :
Summary.

There is a bug in the installer(s): if you uninstall V8 and install V7, the 'CurrentVersion' isn't set correctly, with the result that the registry points to a non-existent folder.

Details.

I was having trouble running some Java programs (not my own) in Windows XP, and in the process I uninstalled and installed Java versions 6, 7, and 8, one at a time, probably in the order 7, 8, 7, 6, 7. The program that had the original problem only worked in V6, but some other programs stopped working. I went back to V7, and those other programs still didn't work. The message was "the registry refers to a nonexistent java runtime environment installation". The only advice I could find with Web searches was to reinstall Java. Needless to say, that didn't work.
So I looked at the registry, and I found that there were still references to V8, which had been uninstalled. The first was
HKEY_CLASSES_ROOT\jarfile\shell\open\command - (Default) = "C:\Program Files\Java\jre1.8.0_31\bin\javaw.exe" -jar "%1" %*
The folder re1.8.0_31 doesn't exist, so I changed it to jre7. That didn't work.
Then I found
HKEY_LOCAL_MACHINE\SOFTWARE\JavaSoft\Java Runtime Environment - CurrentVersion = 1.8
I changed this to 1.7, and deleted some following entries such as
HKEY_LOCAL_MACHINE\SOFTWARE\JavaSoft\Java Runtime Environment\1.8 - JavaHome = C:\Program Files\Java\jre1.8.0_31
retaining entries such as
HKEY_LOCAL_MACHINE\SOFTWARE\JavaSoft\Java Runtime Environment\1.7 - JavaHome = C:\Program Files\Java\jre7
That worked.



ERROR MESSAGES/STACK TRACES THAT OCCUR :
the registry refers to a nonexistent java runtime environment installation

REPRODUCIBILITY :
This bug can be reproduced always.

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Anything.
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CUSTOMER SUBMITTED WORKAROUND :
Manually edit the registry, as described above.