Q: Screen gone black and computer beeps

Seems like you may have loose or faulty RAM:

Beeps on startup:

1 beep = no RAM installed

2 beeps = incompatible RAM types

3 beeps = no good banks

4 beeps = no good boot images.

5 beeps = processor is not usable

http://support.apple.com/kb/HT2538

These beeps show that the RAM is damaged > http://support.apple.com/kb/ht2538

If your iMac is in warranty, take it to an Apple Store or reseller so it will be repaired free of charge. If it's not in warranty, you can try replacing the RAM yourself.

You can buy RAM at OWC or Crucial > http://www.macsales.com Choose RAM, select iMac and your model, so you will be able to get the correct memory. Also, Crucial will do that automatically.

Then, follow the steps to install RAM > http://support.apple.com/kb/HT1423?viewlocale=en_US

If after installing the RAM the Mac works correctly, the problem is fixed. If the problem still appears, the problem is related to the slots, so make a backup of your files and take the iMac to an Apple Store

sounds like a diagnostic code, strange that it boots and works before you get it. is it happening every time you start the computer? can you run Apple Hardware test? If I had to guess I would say bad RAM or memory bank.

It can happen at any moment, so this doesn't change the problem you have, that is related to damaged RAM