How can I get a hold of my iCloud verification code if my old phone doesn’t work?

You can't. You need another Trusted device (a device or computer you have already signed into your iCloud with and have Trusted), or another phone number to receive the Verification code.

If you do not have a trusted phone number or trusted device where you can receive a Verification Code, then you have to request account recovery to recover use of your Apple account. Account recovery can take several days or a week, so you will have to be patient. Apple cannot expedite the process:

If I can't sign in, how do I regain access to my account?

If you can’t sign in, reset your password, or receive verification codes, you can request account recovery to regain access to your account. Account recovery is an automatic process designed to get you back in to your account as quickly as possible while denying access to anyone who might be pretending to be you. It might take a few days—or longer—depending on what specific account information you can provide to verify your identity.

Once you do regain access, I would strongly advise that you add several other phone numbers to your Trusted Numbers list. They can be the phone number of anyone you trust - your Mom, your BFF, your Aunt Bertha. And it doesn't have to be an iPhone. It can be an Android phone or a landline. Just get at least two or three numbers listed so you have a backup in this sort of situation.

Best of luck,

GB