The partition of the hard drive is corrupted, that is why you are unable to install on it. Since it is corrupted, you will have to erase (format) the hard drive.
You have three options in here. First is, buy Disk Warrior (powerful disk utility application) and try to repair your hard disk or recover your files with it. If it is unable to fix the hard drive, then it will at least help you to recover the files that are readable and save them to an external drive. Get it from here : http://www.alsoft.com/diskwarrior/
Disk Warrior is costly. If you don't want to recover any files, then you don't have to buy Disk Warrior. It is not worth it if you don't have any important files/applications.
Second is, you can erase the hard drive and try to do a fresh version of Mac OS X in it. This will erase everything from your hard disk unfortunately. Boot into the Mac OS X Utilities screen just like you did before. In there, select Disk Utility. In Disk Utility, select your hard disk and erase it. Then close Disk Utility and continue installation. This is the quickest solution if you don't mind losing the files in it.
Third is, you can take the Mac to the Apple Store. They will recover the files using their tools and then reinstall Mac OS X for you.
Please let me know what you think.