@shep29,
Have you tried resetting the panel? You might also try disarming the system from the keypad a couple of times in a row. I've had to do this following an alarm to clear everything, the second time clears the fault memory or something. I imagine you wouldn't be able to arm it if this was the case but it can't hurt to try anyway.
Also, this may seem like a dumb question but have you checked to ensure nothing is disabled via the checkbox under the advanced tab? I would check the zones (child devices) as well as the panel and partition devices. I know you said it is arming and disarming but I'm running out of ideas.
Sounds like you may need to dig into the logs to analyze the messages from the panel first. If you can confirm that those zones aren't somehow being reported as faulted then @mcvflorin will probably need to step in and help you.
Hoping @mcvflorin will jump in here soon...
kbmcguire