Running out of disk space with Bitcoin Core
How are you? WOW guessing you're rich now!
The proof you have bitcoin in your wallet does nothing. Bitcoin is not a system you can go and get your wallet back with showing them you have bitcoin in your wallet.
Go to blockchain.info and download the app. Click on add address. Scan your private key and then you can use your bitcoins again.
Hope you can gain access to your wallet.