I created a paper wallet using bitaddress.org and spent bitcoins into it using the Coinbase mobile (Android App). I then noticed that the paper wallet cut off part of the private key during printing! They don't leave anough room for the entire private key. I need to get those bitcoins back out of that wallet/address using only the QR code. I can't figure out how to use the Coinbase mobile app to do that. It apparently can send to a QR code, but not receive from one.
I found another Android app called "Bitcoin Wallet" that let me "sweep" the paper wallet into another address. Everything is fine.
Well, if the private key was lost, then the whole wallet is lost forever, as no one can calculate the private key using part of it or using the public key. The bitcoin address you sent using coinbase is just a hash from the public key, so no use. But if your paper wallet provider generates the private key using the parent key, probably you can ask for their support, but there is little hope.