What model is this? You can check with the serial number on the bottom of the foot. Go to [https://support.apple.com/en_US/specs/imac|this page] and choose "Browse by product" and enter your serial number.
If someone has opened it and you say the the screen cable (LVDS) was damaged, it seems it maybe was not inserted correctly on the logic board side. Also it could be damaged again inserting it incorrectly. If you can open the iMac and tilt the screen so you can see the 4 LED lights beside the LVDS connector you can tell us what light are on. LED 1, 2 and 3 should light up. Then LED 4 should light up and then off.
The crazy fan blowing indicates that a cable is not attached correctly, maybe the temp sensor to the hard drive or LCD. Take a look at [guide|6288|this guide] and check that all the cables are attached. Could be going over the cables again could solve your problem.