Hyundai 2001 engine light stays on

take it to a dealership this car has a recall to check the engine for noise and replacement is does not pass the process tests it is campaign 132 per Hyundai if it has been performed and passed Hyundai will still check engine issues and make possible goodwill repairs BUT this is speculation until know problem with engine/car has been diagnosed

the .pcm puts it in limp mode and it will stay in mode until light is turned off. You need to get the trouble code, repair it, erase the codes (with a scanner that retrieves the codes), and then you will be out of limp home mode.

Easy, find someone that has an OBD2 meter and get the error code # ( an example is Po256) Then plug the code number into google and it will tell you what is wrong.
You have to have a sensor on the engine component for the ck engine lite to come on. Leaking fluid will usually not have a sensor, so this is not the engine light problem.

The noise you hear could very well be a lifter. But that is not what is causing your engine light to come on. The engine light problem can be diagnosed by having the codes read. You can have this done for free at most national parts chains such as Advance or Auto Zone. Good luck! I hope you find this to be very helpful!

Perhaps the cv joint.

your guess is as good as anyones. Someone will have to look at this in person.

Did the 'Check Engine' Light come ON? Whenever the 'CHECK ENGINE' light comes on, the ECU (Engine Control Unit) sets a Diagnostic Trouble Code (DTC). These codes identify the particular engine management system which caused the light to come on.
You'll need to use/find an OBDII (On-Board Diagnostic) Scanner to retrieve any code which have been stored in the ECU computer. Afterward, we might be able to help you DIAGNOSE and perhaps eventually fix the problem.

First of all, there are far too many possible causes for the symptom you describe. Did the 'Check Engine' Light come ON? Whenever the 'CHECK ENGINE' light comes on, the ECU (Engine Control Unit) sets a Diagnostic Trouble Code (DTC). These codes identify the particular engine management system which caused the light to come on. You'll need to use/find an OBDII (On-Board Diagnostic) Scanner to retrieve any code which have been stored in the ECU computer. Afterward, we might be able to help you DIAGNOSE and perhaps eventually fix the problem.

valve cover gasket is leaking replace

Start the car open the hood. with the hood open listen and smell for the leak. Probably the frt exhaust manifold leaking. Independent mechanic can repair just as easy. No need for dealer. If the leak is bad enough you will smell exhause leak. Look for the area with the greatest amount of noise.