Thank you for providing the message you're receiving, mattfrompearland. It's appreciated! Since you're able to use your current password at the Apple ID site, but you're unable to verify it on your iPhone, I'd like for you to contact Account Security for further support.
Contact Apple for help with Apple ID account security -- Account Security has the tools required to verify your identity and help enable your Apple ID. After selecting the link, choose the country or region you're located in and give them a call.
Cheers!