Do you mean the hard drive is mechanically broken for sure? It's not a data corruption issue that is causing a problem with starting up the Mac, but maybe not be a bad mechanism?
If the drive is definitely broken, there are businesses that specialize in recovering data from bad hard drives. For example
http://www.drivesaverdatarecovery.com/ (I always saw their booth at MacWorld Expos...)
The cost of such services is usually high.
cannot get into the computer
So that probably means the hard drive in question is the internal drive? If you don't know for sure that the hard drive is physically broken, you can try starting up using your Mac OS X installation disc. Insert disc in optical drive and start up with the C key held down. When you get to Installer's screen, go up to the menu bar and run Disk Utility from the Utilities menu. Does the internal drive appear in the Disk Utility sidebar?
Alternately, if you have another Mac (that has FireWire), you can try starting the Mac with the problem in FireWire Target Disk Mode,
http://support.apple.com/kb/HT1661
Connect the "target" Mac to the other Mac (running normally) using a FireWire cable. Run Disk Utility on that Mac. Does the hard drive of the Mac in FireWire Target Disk Mode appear in the sidebar?
If you can get the internal drive to appear in Disk Utility, you may be able to run Repair Disk on the First Aid tab. There are also third-party utilities, such as TechTool Pro (Micromat), Drive Genius (Prosoft), and Disk Warrior (Alsoft), that may be able to fix (or at least recover data from) the hard drive.