iMac 27 mid-2011 and Apple Cinema Display 30 (2005)

This isn't because the Graphics card is too old/too slow. 512MB is WAY enough. You might have a problem with the adapters or the Apple Cinema Display causing the iMac to crash, likely because of a software incompatibility.

You could try looking in the System Information App, but I can't advocate that you will be able to resolve your issue from there.

Well it happens sometimes with older hardware, but is should work nonetheless. You confirm that you are using a mini-display-port-to-DVI adapter which then connects to the ADC-to-DVI converter?

i've found some reference on internet, but it all dates back from 5+ years ago, when people were switching from G4/5 PowerMacs to MacPros, and they talk about changing the Graphics card of the Mac Pro's but since then, the technology must have been integrated into the chips, unless intel dropped all support for DVI, which would seem quite weird.

Powermac G4 ADC Display Problem

http://www.macobserver.com/tmo/article/using_older_apple_adc_displays_with_mac_p ro

Display problem ADC

there was at one point a discussion about that an update to 10.7.1/2 has affected ADC support. , which dates back 4-5 years ago.

Some manage to solve the issue by decreasing slightly the external resolution, never knowing why it solved. You might want to try it.

later... just found this, but it isn't updated anymore, and doesn't deal with the 30 inch model :Apple DVI to ADC Adapter: Compatibility Table

An hour later...: I found at last the document I was looking for: OS X Mavericks: Using brightness controls with vintage and obsolete displays - Apple Support

Basically, it says that it won't work with Macs under Yosemite and Mavericks, so it seems they've dropped the technology completely.

Soooooorry 😟

That explains why for more than a year, no one has been talking about it.

So basically, I was right since the beginning, I just couldn't find why it wasn't working.

yeah well then there's nothing to do for it being slow...