I have a 2005 hyundai accent and while driving I lost power and the engine stopped. When you turn the key, the engine turns but does not start, what could be the problem? Could it be the fuel filter or the fuel pump or could it be that there is no spark? Thank you steve

Make sure the brake lights are coming on if not the release solenoid that unlocks park gets no power and will not release the shifter from park position. Also check the owner's manual for a possible way to override the solenoid lock.

Check your starter relay fuse..... New battery....

if the engine has stopped and when you try to start, it turns over fast but no ignition is looks like your timing belt has gone. open the bonnet and open the oil filler cap. with second person starting the engine. ifyou look inside where the oil gets filled and you you dont see the cam turning this indicates the belt is not turing. if it is turning then it is a different issue. these belts should be changed at set periods on your service schedule usually around 100000 miles. you might be luck if this is the case that only the belt needs to be put on and timing set up. if not you may have a damaged engine as the pistons may have hit valves as they where not syncronised due to the belt failure.

i hope this was useful

Sounds like a wiring issue from the body to the fuel pump in the gas tank or the fuel pump itself but my guess is a wiring problem there or close to the ECM (computer) inspect the wiring and harness for lumps in the wire or broken wires or corroded connections.
try running a new ground wire from the battery to the Engine and the body of the car - a simple task . then run a ground wire directly to the gas tank but dont make any holes in the tank or weld upon it lol.

You'll have to figure out if it is a fuel or ignition problem.
Check and see if you are getting spark to the plugs first.
Also re-check the computer for codes and see how many are back.
Trouble codes are suggestions, not solid instructions.

Try hooking your seat belt, put it on, before you try to start the car.

remove one of your spark plugs and have some one turn it over you stick your finger into the spark plug hole if compression pushes it out then its not your timing belt if it doesn't push it out than replace your timing belt

I have a 2006 Accent and also to me sometimes the eps light turn on while I'm driving. I turn off the car and wait few seconds before to turn on again. But how to repair this problem?

bad battery ( have a load test done
faulty ignition switch

Put a fuel pressure guage on the test port on fuel rail. With fuel injected engines if pressure is too high or low car wont start.
Cycle key off to run (not start) you should hear the pump run a few seconds and stop.