What if I receive a bitcoin when my computer is powered off?
This works fine. The bitcoins will appear next time you start your wallet application. Bitcoins are not actually received by the software on your computer, they are appended to a public ledger that is shared between all the devices on the network. If you are sent bitcoins when your wallet client program is not running and you later launch it, it will download blocks and catch up with any transactions it did not already know about, and the bitcoins will eventually appear as if they were just received in real time. Your wallet is only needed when you wish to spend bitcoins.