I have an article here for you that should be able to walk you though some troubleshooting steps for this issue:
Keep in mind that in the course of troubleshooting this issue, you may need to troubleshoot any cables or adaptors you are using as well. If the steps in the article do not help you resolve the issue, then you may need to follow the suggestions at the end of the article:
Helpful related articles
These articles may offer additional assistance and information about displays and video adapters:
- Apple Portables: How to use your computer in closed clamshell (display closed) mode with an external display
- Apple Cinema Display (30-inch DVI) has 1280 x 800 as the maximum available resolution
- Mac Pro (Early 2009), Mac Pro (Mid 2010): Supported display configurations
- For assistance with Retina displays, please see Frequently asked questions about using a Retina display.
If you tried all of these steps for your display and the video issues persist, contact Apple technical support or take your Apple computer to the nearest Apple Store or Apple Authorized Service Provider (AASP) for diagnosis. If you plan to visit an Apple Retail Store, make a reservation at the Genius Bar using http://www.apple.com/retail/geniusbar/ (available in some countries only).
Take care, and thanks for visiting the Apple Support Communities.
I tried everything you linked me to, with only one useful result. During PRAM reset the desktop became visible on the projector - but afterward there was again no conenction.
Not only that, but the PRAM reset didn't do what the Apple directions you linked me to said they should - the machine didn't restart after the initial chime, instead it went to a grey utility screen with options like looking for solutions online or starting disk utility. Hopefully it just means the page you linked me to needs to be updated and is for an older OS version.
Incidentally, Safe Mode never came online with the other process - it showed an extended grey apple screen with a load bar along the bottom and once the bar was loaded the computer shut down. I'm hoping this is also normal with the current OS and the page you linked me to was outdated.
This machine came back from Apple about two months ago with almost every part replaced, so it seems unlikely that there is something I need them for. I hope not as I live three hours from the nearest one and mailing it in takes a while.
Hey again ninthname,
Thank you for using the Apple Support Community. Due to the nature of your issue or question you may find more information by using another one of Apple's support resources - https://expresslane.apple.com/GetproductgroupList.action.