You can try Safe Mode:
After the Mac is completely shut down, push the power button and immediately after the startup tone, hold down the Shift key. The Shift key should be held as soon as possible after the startup tone but not before.
Release the Shift key when you see the gray Apple icon and the progress indicator (looks like a spinning gear).
There should be a message that says "Safe Boot." After the Mac is completely booted, try restarting and see if the issue is gone.
But I think you're going to have to buy recovery software and if that doesn't work, then you'll have to send it to a data recovery professional.