What should I do if I forgot my iCloud password?

I have an old computer that barely turns on. Many of my pictures, important pictures, are missing, even though I backed up all my data into an external hard drive. I realized yesterday that the pics are in the cloud. I enter my cloud password, which connects to my current computer and asks me to provide I code, which I did. After that it keeps asking me to enter a password - I don't know what that is or what it is for. You have my IP, my name, my password the code from my current computer, same wife, same name on the computer account and your OVER THE TOP ANNOYING security is still not satisfied with that. this is the message: "cloud preferences wants to make changes to your account. Type your password to allow this." there is no prompt to say I forgot the password. I don't even know what this password is. My old computer is 14 years old.

Please help. You are holding my photos hostage.

[Re-Titled by Moderator]