If the EPU (Emergency Power Unit) and batteries plus engines fail on a modern fighter aircraft, basically they will fall out of the sky, there is no dead stick landing - is this correct?
How Are Modern Fighter Aircraft Controlled?
The F16 was the first US military aircraft to be designed around the revolutionary fly-by-wire concept. This meant there were no direct mechanical linkages between the cockpit and major control surfaces, and that all pilot input was electronically carried to the hydraulic system via wire. However, since the F16 burst into the scene, there have been further major advancements in aircraft systems design. Late Gen 4 aircraft, such as the F/A 18 Super Hornet, are designed around a concept now called control-by-wire. Control-by-wire aircraft not only have removed mechanical linkages to the hydraulic system, but now the pilot is only a voting member. This means that all input is received by a computer bank that then computes what it thinks the pilot is intending to do, and then autonomously operates the control surfaces to achieve the effect. This means that Gen 4 aircraft rely heavily on both computer integrity (and there are plenty of self-healing backups), and the power required to run those systems.
If there was a catastrophic total electrical failure and the only remaining power supply was the battery, the only option is for the pilot to restart a generator. In the event that the engines were operating and all power generation was destroyed, the aircraft would only be flyable for the duration which the battery could provide power to the aircraft--that's a very limited duration.
Possible other scenarios could include a dual-engine failure. In this instance, the aircraft may be able to fly fast enough to generate enough airflow down the turbine to turn the generator and perform an airstart, but this would only be useful in a dual engine failure, and only if there was enough altitude and airspeed to trade to make it a realistic option. Otherwise, the battery would probably be used to power the APU, and attempt a relight. Again, if both engines relit and the generators (including the APU) failed to produce power, then the aircraft would not be flyable.
But what about the RAT?
Although currently in limited use on some trainer aircraft like the T-45, modern fighter aircraft do not use a RAT.
So what usually happens in a total electrical failure?
If the aircrew cannot get a generator back online then they eject.
Define "modern". The A-10 is only 38 years old, is still in service and is expected to remain so until at least 2020 (its planned replacement, along with many other current service aircraft including the F-15E, F-16 and F/A-18, is the much-maligned F-35 program). It has redundant hydraulic systems for all major control surfaces, plus a set of drect cable linkages, so even in a fully unpowered glide a true "dead stick" landing is possible. However, this is probably an unfair example as the A-10 was designed in part for extreme survivability in low-altitude combat conditions where the aircraft could encounter practically everything that airplanes and their pilots don't like, from small-arms fire and flak to short-range ground or air missiles and even a well-aimed tank or artillery round.
"Modern" fly-by-wire jets typically have similar redundancy, but with no direct mechanical link from stick to control surfaces, they are at least partially dependent on electrical power for the flight control computer (in addition to the power required for the hydraulic motors). In the case of a total loss of electrical power, you're right, the aircraft would be uncontrollable until one of two things happened; the pilot got one of the electrical sources back online (typically an engine-powered generator), or he gave up and punched out.
One might wonder how much has to go wrong for the generator coupled to each engine turbine and the APU to fail, leaving the pilot with only battery power for the displays (and to attempt maybe one engine restart). The answer is "a lot"; the most likely scenario causing a simultaneous failure of all generation systems is a missile impact, and in that scenario most fighters wouldn't make it back anyway. However, a failure in the power distribution system of the aircraft might be more likely; this system is redundant as well, but there are some necessary bottlenecks, and one or two relatively minor failures in series could conceivably disable a plane mid-flight.