2000 mazda protege making a squeeling sound when down shifting

Because of the battery light coming on, it sounds like you have a problem on the computer communications network. You need an auto electrician with a pro grade scan tool computer to diagnose. It is very unlikely you need a new transmission.

https://www.google.com/search?q=2000+Mazda+Protege+won%27t+shift+from+3rd+to+4th

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check fuel pressur, filter and fuel pump...sounds like it isnt getting fuel

bad fuel injectors. bad spark plugs - inspect and or replace -- bad spark plug wires - test ohms resistance of the spark plug wires with a multi meter (5 bucks at harbor freight) -- or simply replace the spark plug wires.
How was it you tested the coil and spark at the plugs?

I'd lean more towads faulty fuel injection, if you go to repai this, please be sure to add a quality fuel tank cleaner like lucas (the larger the bottle the less the cost per ounce - and works VERY well), You may also want to be sure to replace the fuel filter...
Best regards
Ck

www.engine-light-help.com/generic-engine-check-light-codes.html

try changining the #3 fuel injector.

Sound like first gear is going out on you. It could also be an issue with the clutch. If the car has enough power try to take off in second gear and see if it hopes. If it doesn't there's likely a problem with first. Unless you are a certified auto mechanic, it's probably best to bring it in and have them conferm that it is a problem with the gear and have them take care of it. It might mean replacing the transmission.

They are the ignition coils, the spark plugs are under them. When you have them off before pulling the spark plugs make sure the holes the plugs are in do not have oil in them, if so you will need new coil boots, plugwires and a valve cover gasket as well.

you mean the #3 fuel injector? start by checking the wire harness that plugs into it. sounds like an internal break in one of the wires. most fuel injectors have power going to them and the pcm grounds each of them individually to make them "fire" the gas charge. it is also possible that the injector is plugged up with debris and you will need to replace the injector. you should have a misfire code for #3 cylinder if you ran a scan with an OBDII error code reader.

Probably your spark plug get wet (water get into your spark plug), so it doesn't work quite well to give high voltage spark to burn fuel.
Clean your spark plug by removing spark plugs of 4 cylinders and clean, start engine to blow out the residue water in spark plug socket. And install spark plug into 4 cylinders

change the transmission fluid, replace the oil and oil filter check spark plug cables, check starter coilpak, and make sure there is coolant