Finally found a forum post that outlined what the registry is supposed to look like when not broken.
- Added key
HKEY_LOCAL_MACHINE\SOFTWARE\JavaSoft\Java Runtime Environment
- Added String Value
CurrentVersion
=1.7
- Added key
HKEY_LOCAL_MACHINE\SOFTWARE\JavaSoft\Java Runtime Environment\1.7
- Added String Value
JavaHome
=C:\Program Files\Java\jre7
Running cmd java -version
and Eclipse now works