Can't buy book- the Buy Book button doesn't appear to work. Any solutions?

Are you using iPhoto 9.6?

Check, if you are connected to the correct Apple Print Products Store:

iPhoto Preferences > Advanced > Print Products Store

The country in this setting needs to be the same as the country of your billing address and delivery address, also your AppleID and Credit Card.

If your country settings are correct, check the setting for your AppleID and enable "Express Checkout" for your Apple ID directly at the Apple Store. You can do this right from the top of this web page.

Look at the black title bar at the top of this page. There is a Store menu to the left. Click it to open the page of the Apple Store. On the next page click the head icon to the left of the shopping cart to open the settings for your account. There you can enable the Express Checkout settings at the link "Update Express Checkout Settings".

Edit and reenter all your billing address and delivery address details on this page.

It's great, that you finally could order your book in time. I hope, it will turn out great 🙂

Only after I restarted the computer did it actually work.

Restarting your computer will clear caches in your temporary directory. Sometimes these caches cannot be written, and then your changed preferences may not take.