Pretty silly question.
Since Bitcoin relies on the internet for transactions, Bitcoin would effectively die.
Absolutely wrong.
There are many offline wallets which donot require internet connections .
Armory wallet can be used for offline transactions but you need some more efforts and hardwork to do so.
To send Bitcoins from your armory offline wallet, do the following:
1. On the online computer, click the
Offline Transactions button on the right, below the logo. Select
Create New Offline Transaction . Alternatively, you can just select
Send Bitcoins and select the watching-only/offline wallet.
2. Create the transaction as you normally would but the “Send” button will be grayed out since the watching-only wallet cannot sign transactions..
3. Click the button Create Unsigned Transaction on the left side.
4. A window will open with the unsigned version of the transaction. Press the Save to file… button to save a
*.unsigned.tx to the USB key
5. Insert USB key in offline computer, and click Offline Transactions , then select Sign or Broadcast Tranasaction.
6. Load the file from the USB key, then press the Sign button. A confirmation window will appear.
7. Verify the confirmation details before you sign it! The benefits of an offline wallet are lost if you don’t make sure the details are correct!
8. Click Save to file… . It will overwrite the original *.unsigned.tx file with a *.signed.tx file.
9. Eject the USB key and plug it into the online computer. If the original window is still open, you can click on Next Step to get to the broadcast window. If you closed Armory since then, you can use the same Offline Transactions button on the main window, and select Sign or Broadcast Transaction . Once the file is loaded, some green text should appear telling you that the signature is valid and the Ready to Broadcast! button should become available.
10. Press the button and you’re done!
Well, I think a majority of people wouldn't know what to do (especially what you just described) if all of this were to go down. The fact is, is that there will be no more miners to confirm transactions to another party you are trying to send bitcoins to, and there for the security of transacting bitcoins to get a good or service when the internet is down is down as well.
The only possible way to transact bitcoins in a secure way if everything were to shut down, in my mind, is to have a cold wallet storage that you can see how much bitcoins is on there, in which you can transact physically... not by some broadcast function of what you said. Though, if this were the case... I don't think people would even want to transact with bitcoins, because Bitcoins economy would essentially be shut down... it's inevitable that Bitcoin is tied to the internet.