This is a test you can make.
First download from below, google play store.
Google Play Store APK 7.0.16.H
I installed Google Play services 3.2.25
You must install google account manager, google play services and google services framework if you don't have it.
Always try to install the closest year for google play store and google play services vs android version.
If you download many version of google play, install the new first. I did it otherway, but it is harder.
Regardless, i cannot install anything on android 4.0.4.