I am a bit confused (which isn't that difficult for me
). You say the client will sync your messages but not display them? how do you know the messages are being synced?
are you trying to setup EXCHANGE emails or just regular pop accounts?
if you want to setup exchange accounts from your job or what have you, there may indeed be some security policies in place. the IT section of the department managing the exchange accounts will help you with this.
if you have success with a 3rd party app (mail.com) why not just use that and be done with it?
are you rooted?
what carrier are you using?
if you want some recommendations on 3rd party app clients, head over to the app section:
Android Applications - Android Forums