If the application installer is 32 bit and your OS is 64 bit, when it thinks it's looking in Windows\system32 it's actually looking in Windows\SysWow64 due to 32 bit emulation.
Since you have 12 GB ram and home premium I'm assuming for now that it's a pre-installed OS and would therefore be 64 bit. But please post/fill in data/ as A Guy requested.