In an event of failure of all engines of a commercial aircraft in mid air and no secondary backup or generators powering the plane (plane is virtually powerless and no comp systems work on board), would the ATC still be able to detect the aircraft with accuracy and if yes how is it done ? Are there any conditions that it has to be flying in an area which is monitored or any basic stuff which HAS to be working for ATC to detect ?
In an event of failure of all engines of a commercial aircraft in mid air ...
That would be a very rare event. In the modern cases where this has happened within an ATC area, it has not prevented location of the aircraft so far as I know.
... and no secondary backup or generators powering the plane
Even a two-engined airliner has an Auxiliary Power Unit (APU) and a Ram-Air Turbine(RAT). I believe they also typically have 10-15 minutes battery power for critical systems. I don't know if any airliner has ever lost all generators other than in cases where the aircraft was destroyed in flight (e.g. PanAm 103).
would the ATC still be able to detect the aircraft with accuracy
If an aircraft's transponder and secondary-radar are not operating, ATC would rely on primary radar, which is less accurate, particularly for altitude. They would also ask the pilots for their position over VHF radio and ask other aircraft in the area to locate the aircraft.
Example: British Airways Flight 9
All four engines flamed out due to ingestion of volcanic ash.
Despite the crew "squawking" the emergency transponder setting of 7700, the aeroplane could not be located by Air Traffic Control on their radar screens.
The pilot communicated with ATC over VHF radio and later restarted the engines.
The engines had enough electrical power to restart because one generator and the onboard batteries were still operating
Example Air Canada Flight 143 (the "Gimli Glider")
This 767 ran out of fuel mid-air and all engines stopped.
The 767 was one of the first airliners to include an Electronic Flight Instrument System (EFIS), which operated on the electricity generated by the aircraft's jet engines. With both engines stopped, the system went dead, leaving only a few basic battery-powered emergency flight instruments.
The pilot communicated with ATC Winnipeg and
First Officer Maurice Quintal began to calculate whether they could reach Winnipeg. He used the altitude from one of the mechanical backup instruments, while the distance traveled was supplied by the air traffic controllers in Winnipeg, measuring the distance the aircraft's echo moved on their radar screens.
So yes, If the aircraft with all engines out is in radar range and ATC are attentive, they can track the aircraft's location.
Primary radar (send out radio pulse and interpret reflections) was designed for this (detect uncooperative enemy aircraft).
A more complete explanation of this system can be found on the answers of this question.
Having said that, when all engines fail the backup is a Ram Air Turbine which gets deployed automatically and provides enough power for critical systems including controlling the craft, radio and transponder. Having every backup fail is extremely unlikely.
RAdio Detection And Ranging do not require active participation from the airplane, so ATC will still see it. However, ATC will not know of the plane's condition and will likely not be able to communicate with them.
Pretty much, if the craft is made out of metal and is reasonably high in the air, ATC will see it. Most non-metals will show up on radar as well, such as this guy.