Q: screen goes black after installing Mountain Lion or Yosemite

Add more RAM to your computer. 2 GBs is simply not enough, but that isn't the cause of the problem.

Reinstalling OS X Without Erasing the Drive

Boot to the Recovery HD: Restart the computer and after the chime press and hold down the COMMAND and R keys until the menu screen appears. Alternatively, restart the computer and after the chime press and hold down the OPTION key until the boot manager screen appears. Select the Recovery HD and click on the downward pointing arrow button.

Reinstalling OS X Without Erasing the Drive

Repair the Hard Drive and Permissions: Upon startup select Disk Utility from the main menu. Repair the Hard Drive and Permissions as follows.

When the recovery menu appears select Disk Utility and press the Continue button. After Disk Utility loads select the Macintosh HD entry from the the left side list.  Click on the First Aid tab, then click on the Repair Disk button. If Disk Utility reports any errors that have been fixed, then re-run Repair Disk until no errors are reported. If no errors are reported click on the Repair Permissions button. Wait until the operation completes, then quit Disk Utility and return to the main menu.

Reinstall OS X: Select Reinstall OS X and click on the Continue button.

Note: You will need an active Internet connection. I suggest using Ethernet if possible because it is three times faster than wireless.

Alternatively, see:

Reinstall OS X Without Erasing the Drive

Choose the version you have installed now:

OS X Mountain Lion- Reinstall OS X

     Note: You will need an active Internet connection. I suggest using Ethernet

                 if possible because it is three times faster than wireless.

To find the model identifier open System Profiler in the Utilities folder. It's displayed in the panel on the right. Please post it. or see,

Upgrading to Yosemite

You can upgrade to Yosemite from Lion or directly from Snow Leopard. Yosemite can be downloaded from the Mac App Store for FREE.

Upgrading to Yosemite

To upgrade to Yosemite you must have Snow Leopard 10.6.8 or Lion installed. Download Yosemite from the App Store. Sign in using your Apple ID. Yosemite is free. The file is quite large, over 5 GBs, so allow some time to download. It would be preferable to use Ethernet because it is nearly four times faster than wireless.

    OS X Mavericks/Yosemite- System Requirements

      Macs that can be upgraded to OS X Yosemite

         1. iMac (Mid 2007 or newer) - Model Identifier 7,1 or later

         2. MacBook (Late 2008 Aluminum, or Early 2009 or newer) - Model Identifier 5,1 or later

         3. MacBook Pro (Mid/Late 2007 or newer) - Model Identifier 3,1 or later

         4. MacBook Air (Late 2008 or newer) - Model Identifier 2,1 or later

         5. Mac mini (Early 2009 or newer) - Model Identifier 3,1 or later

         6. Mac Pro (Early 2008 or newer) - Model Identifier 3,1 or later

         7. Xserve (Early 2009) - Model Identifier 3,1 or later

To find the model identifier open System Profiler in the Utilities folder. It's displayed in the panel on the right.

     Are my applications compatible?

         See App Compatibility Table - RoaringApps.

You can install all the way to Yosemite. You will need to re-install it Yosemite or Mountain Lion - your choice.

There may be a hardware failure. Please make a Genius Appointment and take it in for service to find out.

Try adding RAM. The 2 places I’ve seen recommended most to buy reliable RAM are below. I have purchased RAM several times from Other World Computing and have always been very satisfied with the product and service. They have on-line instructions on how to replace the RAM. OWC has also tested RAM above what Apple states is the maximum. I now have 6GB installed on a early 2008 iMac supposedly limited to 4 GB and noticed an improvement.

Crucial

Other World Computing

You are welcome. Yosemite and Snow Leopard (2 partitions). No problem with either.