I am in Italy and my credit card broke into three pieces. I have a US bank account. I know my account number. I didn't register for international transfer before leaving the US. What can I do to get money from my US bank account?
To get a replacement physical card you can either:
Contact your US bank, or, you can also contact the emergency toll-free number from your credit card brand; this is likely preferable as they can coordinate a replacement around the world, which your bank may not do as fast.
You can contact Customer Service when traveling outside of the U.S. by calling (country code) +1-801-902-3100. This number also appears on the back of your Discover Card. Please be sure to retain this number with your travel documents. You also can report your card lost or stolen online. Please click the link to report your card lost or stolen.
As a temporary measure, or if you can't secure a new card in time before you return home, assuming you have a participating bank and mobile phone, you can use Apple/Google/Samsung... Pay, it is accepted nearly everywhere they accept cards due to the dual use terminals (some older terminals may not have it though).
For AMEX for example, they advertise that as soon that your replacement request is placed, they will update your wallet app remotely, so that you can continue using it while your card is shipped
What can I do to get money from my US bank ??
You can still use the card online to buy flight ticket, order food/Uber, send cash to yourself via Western Union, buy some skype credits to call your bank for more ideas, etc. Also try taping/gluing the card to see if it works with a chip reader or magnetic stripe reader, and check if it works contactless. You have 3 cards now, that should give you more options.
Did the magnetic stripe and/or chip break? I haven't been to Italy, but I guess that in many shops you'll just need to insert the chip in their machines, it doesn't go very far in. If the magnetic stripe is intact, it should be relatively easy to swipe it through the machines. In any case: if it looks likely that you'll be able to extract it (the part of the card you use) again I don't think the people in the shop will care much, especially if you explain the situation and ask before shopping.