Computer broke, how to obtain the private key?
First, backup your wallet.dat file (if you don't know where it is stored, check this: https://en.bitcoin.it/wiki/Data_directory)
Analyse the crash, read the error message.
Quit Bitcoin-Core, try to temporarily move your data-directoy and let bitcoin-core create a new one.
Quit Bitcoin-Core, replace the newly created wallet.dat file with your old one (after you made a backup)
Start Bitcoin-Core again
If you don't want to wait until your full-node is synced (can take a couple of days), export your private key by opening the Development Console (ctrl - D in 0.13.0) and type dumpwallet &lt;path + filename&gt;