I can understand it. But, actually, the user profile folder of your system is corrupted and that is why you are not getting the option to login to the user account.
If you have the installation disk, please use Disk Utility
to Repair Disk
and the Repair Disk Permissions.
It will fix the issue. Check this tutorial
to see how to use disk utility for these functions.
If it not helps, you need to re-install mac osx. Your files and settings will not be touched as long as you don't specifically tell the installer to erase them. Follow below steps to re-install osx.
1. Insert your Mac OS X Install DVD or Installation Disc 1.
2. Restart the computer and hold down the letter "C" as the computer starts up.
3. Continue to hold down the letter "C" until you see a grey screen with an Apple and a small spinning gear.
4. Select your language on the Welcome to the Mac OS X Installer screen and click "Continue".
5. Click "Continue" on the following screen.
6. After reading the Software License Agreement, click "Agree".
7. Select the volume to which you are going to install. "Macintosh HD" is the default name.
8. Click the "Options" button in the bottom corner of the window and select your installation type.
9. Click "OK" and then "Continue". You will be presented with a confirmation window at which point you can click "Install" to proceed.
I am sure re-install will fix the issue. Try and let me know the result.