Booting into Mac OS stalls at about 75%

A Troubleshooting Procedure that may Fix Problems With Lion to Yosemite

You should try each, one at a time, then test to see if the problem is fixed before going on to the next.

Be sure to backup your files before proceeding if possible.

1. Shut down the computer. Disconnect any third-party peripherals.
2. Reset your Mac's PRAM and NVRAM
3. Intel-based Macs: Resetting the System Management Controller (SMC)
4. Start the computer in Safe Mode. Test in safe mode to see if the problem persists, then restart normally. This is slower than a standard startup.
5. Repair the disk by booting from the Recovery HD. Immediately after the chime hold down the Command and R keys until the Utility Menu appears. Choose Disk Utility and click on the Continue button. After Disk Utility loads select the hard drive entry (mfgr.'s ID and drive size) from the side list. In the Disk Utility status area, you will see an entry for the S.M.A.R.T. status of the hard drive. If it does not say "Verified" then the hard drive is failing or failed. (S.M.A.R.T status is not reported for external drives.) If the drive is "Verified" then select the indented (usually, Macintosh HD) volume from the list. Click on the First Aid tab, then click on the Repair Disk button. When it finishes then click on the Repair Permissions button. When that has completed quit Disk Utility and return to the Utility Menu. Select Restart from the Apple menu.
6. Run the Apple Hardware Test. Use Apple Hardware Test and How to invoke and interpret the Apple hardware tests - CNET.
7. Create a New User Account Open Users & Groups preferences. Click on the lock icon and enter your Admin password when prompted. On the left under Current User click on the Add [+] button below Login Options. Setup a new Admin user account. Upon completion log out of your current account then log into the new account. If your problems cease, then consider switching to the new account and transferring your files to it - Transferring files from one User Account to another.
8. Reinstall OS X by booting from the Recovery HD using the Command and R keys. When the Utility Menu appears select Reinstall OS X then click on the Continue button.
9. Erase and Install OS X Restart the computer. Immediately after the chime hold down the CommandandRkeys until the Apple logo appears. When the Utility Menu appears:

1. Select Disk Utility from the Utility Menu and click on Continue button.
2. When Disk Utility loads select the drive (out-dented entry) from the Device list.
3. Click on the Partition tab in Disk Utility's main window toolbar.
4. Set the number of partitions to one (1) from the Partition Scheme dropdown menu.
5. Set the Format type to Mac OS Extended (Journaled.)
6. Click on the Apply button.
7. Quit Disk Utility and return to the Utility Menu
8. Select Restart from the Apple Menu.

If none of the above helps then make an appointment at the Apple Genius Bar for service. If you need to find an Apple Store - Find a Store - Apple.

Attempt restarting in Safe Mode per Use safe mode to isolate issues with your Mac - Apple Support if that does not work then restart in the Recovery Partition and run First Aide and see if any errors appear. I suspect if a Safe Mode restart does not work another component has failed, considering the age of the computer you have to decide what you want to do.

That machine came with two recovery DVDs on which is also the AHT. Without those disks you can't run the AHT by using 'D' during startup.

Glad to help. Have a great weekend.