2003 Elantra does not start. New battery.

Question edited for clarity.

Possibly, some do cover things that affect starting, the 'fuel pump relay' for instance. You need to diagnose, not just replace as a guess. Check for codes. A prograde scan tool will diagnose all modules and relays.

https://www.autogenius.info/hyundai-elantra-2005-fuse-box-diagram/

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Look for a hose coming out of your firewall running down to the bottom of the car

Have u checked the main fuse in the car? Should b like an 80amper, good luck!

disconnect the earth wire from the battery and place a multi meter in the circuit and read the current draw through the current (AMPs) section of the meter. That will tell you what is drawing current and how much.. Things to check include the glove box light is off, boot light is off. the radio amp is off when the ignition is off. When you have done that hook the multimeter across the battery after replacing the earth wire ( red lead to positive and black lead to negative) and start the engine hold RPM at around 1200 and read the voltage in the battery It should be 14.5 volts dc now set the multimeter to read ac and see if you have any voltage there IT should be 0 voltage . That will show that the alternator and rectifier diodes are ok. Check that the drive belt is in good condition and tensioned right.. You say 3 batteries in 13 months . How many have been brand new out of the battery shop type and how many are new to you from some place else. If they have not been new as off the shelf new then have a load test done on the battery as it may have an internal short

P2626 O2 Sensor Pumping Current Trim Circuit/Open (Bank 1 Sensor 1)

I'll sure this has to do with a faulty O2 sensor. This sensor is usually located around the header of your car, or down more on your exhaust.

Try disconnecting your battery for 30 mins, hook it back up, and start your car again. This will erase the error. See if it comes in again.

Hope this help (remember rated this post).

Did you use a aftermarket O2 sensor or a genuine Hyundai one? If it's an aftermarket one it may be bad or not as good as the OEM one. See here for more details and other potential causes: P0133

Hi:
If you follow your upper radiator hose back to where it attaches to the engine, that is where the thermostat is located. it is called the thermostat housing and it is held onto the engine with 2 or 3 bolts. If you purchase the thermostat from an auto parts store, they often can give you some specific guidance too. Of course, you need to start this project with the engine cold, and first drain the coolant out of the system. Make sure you have a new gasket or sealant to install teh new thermostat too.

If the car is turning over but won't stay running, it is not the ignition switch. You also said it is "trembling very badly" when it is turning over, this leads me to believe that it might just be moisture under the distributor cap or a bit of carbon build up on the rotor.
Try this: remove the distributor cap WITHOUT REMOVING ANY OF THE WIRES. There are 2 screws that hold it in place, loosen them and turn the cap over to look inside - if you see any moisture, wipe it out with a dry rag. Next inspect the rotor, that's the piece still on the engine under the cap, on the end of it is a metal contact. If it is at all blackened (carbon build up) either LIGHTLY scrape it with a flat blade screwdriver or LIGHTLY sand it until shiny with fine grit sandpaper. Put the cap back on, retighten the screws to secure it, and see if that gets it to start.

Amazing!.. Belts don't 'ignite!' Never have and never will. Find yourself a good mechanic/technician and get them to look at it.

what u do is go to your local auto supply store and buy throttlebody cleaner you remove the rubber hose from the throttle body with the engine off of course u open the throttle and spray cleaner in it then use a tooth brush inside it replace the hose done
except it will be hard to start the first time crank engine over with foot to the floor on the gas pedal do not pump it