"Incompatible with other applications(s) using the same shared user ID" when installing Google Play service?

I need to run Google Plus, and Google Plus needs the Google Play service.

Every time I install google play service from the Google Play store it fails to install with this error:

Incompatible with other applications(s) using the same shared user ID

What could be the issue? How can I fix this?

^{UPDATE: I know almost nothing about android, so I dont know what ROM is, or such thing, I get my phone from local production and I guess, yes, it uses custom system, so I just know that I'm using Android Version 4.0.4. any help would be greatly appreciated.}