If you change your password when off campus you'll need to connect to the VPN then lock your account(Windows key+L) and log back in before you can log into your machine using your new password.
Normally, when you log into a domain joined machine, the credentials you supply are passed to the nearest domain controller for verification. If your machine can't reach the Domain Controllers (e.g. you're off campus) and you've previously logged into this machine then a version of your password is cached locally on your machine. When you attempt to log in, your supplied credentials are compared to that hash and, should they match, you're allowed to log into the device.
Unfortunately, if you change your password at https://identity.uillinois.edu these two copies of your credentials are no longer in sync and your machine can't contact the domain controllers to verify your credentials. If you try and log into your machine using your new password, then it will be compared with the cached version stored on your machine and you'll be unable to log in.
To be able to log into your machine using your new password you need to:
1. Log in to the machine with your old password (cached credentials)
2. Connect to your network then log in to UIC VPN with your new password
3. Lock your Windows session (Windows key + L, or CTRL+ALT+DELETE then select Lock)
4. Log back in to unlock it using your new password
5. Log out
You should be log back in using your new password.