There are working combinations of OS, JDK and Eclipse bitness. In my case, I was using a 64-bit JDK with a 32-bit Eclipse on a 64-bit OS. After downgrading the JDK to 32-bit, Eclipse started working.
Use one of the following combinations.
32-bit OS, 32-bit JDK, 32-bit Eclipse (32-bit only)
64-bit OS, 32-bit JDK, 32-bit Eclipse
64-bit OS, 64-bit JDK, 64-bit Eclipse (64-bit only)