Q: mavericks installed but will not go to login

Startup - Gray, Blue or White screen at boot, w/spinner/progress bar

Startup - Gray Screen

Startup Issues - Resolve

Startup Issues - Resolve (2)

Startup – Computer Stops or Delays

Boot to the Recovery Volume (command - R on a restart or hold down the option key during a restart and select Recovery Volume). Run Disk Utility Verify/Repair and Repair Permissions until you get no errors.

OS X Recovery

OS X Recovery (2)

Do you have access to another Mac?

'Target disk mode' can allow you to read the internal HD from another Mac if you have the right connectors & cables…

http://support.apple.com/kb/HT1661

I'd also reset the PRAM

https://support.apple.com/kb/HT1379

Boot to safe mode

https://support.apple.com/kb/HT1455

You may also be able to boot from a backup disk if you have a full bootable clone available. That can also allow you to view the files on the Mac's internal HD.