When I returned to iOS I was using Exchange. I set up my Exchange account by selecting Gmail Set up Google Sync with your iOS device - Google Apps Help
I no longer use Exchange and I'm not sure that Gmail still supports the process in the link.
Have you verified with the sys admin that your password and account settings are correct?
When I use gmail it doesn't sync contacts. I'm unsure what you mean by sys admin? I know my password is correct.