Had the battery of 2004 santa fe replaced now the malfunction light won't go off.

All vehicles made for the last 35 years have a
malfunction indicator light (1981 thru 2015)

Have you not read your owners manual?

Battery voltage is high, suspect alternator over charging and affecting the monitor. Connect an external volt meter across the battery and start engine 15volts or above will cause problems. If left charging high, it can shorten the life of the battery and damage electronics of the vehicle, things like abnormal amount of bulbs blowing. All electrical equipment is made to operate at around 13 volts with a percentage tolerance, constant running at a higher voltage will cause damage.

I would go ahead and have the computer scanned for trouble codes, hopefully something is stored in the computer memory.

It takes a special scanner to retrive this code, a generic handheld won't get it,

650 CCA  (cold cranking amp) battery.

Made a video of me replacing the brake light but I show how to remove and install the tail light assembly. It's on a 2005 Hyundai Santa Fe but should be the same as a 2004.

What does that mean? Go to www.hmaservice.com and register( Vehicle by VIN). Afterward, you have access to shop manuals, service bulletins, wiring diagrams, etc. about your vehicle.

Have your alternator and alternatorwiring checked, if the ALT light goes on, so does the brake. So it could be that the alternator is faulty. Also check the fuses.

possibly 1 of the fuel injectors is malfunctioning causing a fuel lock,try getting them tested

If you mean the "check engine" light (yellow) next to the "cruise" light if you have cruise control, you need to have the code scanned to find out what the erroe code is. From there, you will know how it can be fixed. I've been told that as long as the light doesn't flash, you can still drive the car. An auto parts store probably can read the code for you because they will want to sell you the replacement parts.