Intel 64 bit processor running Windows 7 64 bit. Clean install of LibreOffice 3.5.5.3. Clean install of Java 1.7, 32 bit. Base fails to open tables and reports a defective JRE. (Similar results if the 64 bit Java 1.7 is used - but many comments point to the need for 32 bit Java.) I added an installation of Java 1.6. (It is on the Java.com site http://java.com/en/download/manual_v6.jsp.) I used the Tools/Options/Java selection to select use of the 1.6 JRE and now Base loads and edits tables without issue.
All links I have appended seem to show the same problem. And all this bugs were marked as "Unconfirmed". I can't confirm, because I have no Windows-System here. Would be better to search the database of freedesktop org, for example "libreoffice → database → java" and confirm the bugs other persons have reported. Could you please have a look at the other bugs and push it to new, if it is a bug you can confirm? Then you could change this bug to a duplicate of the other bug.
*** This bug has been marked as a duplicate of bug 47177 ***