2004 Mazda 3 2.3L
140,000+ miles

I was driving down the highway and my car drove like normal. I turned into a street and realized I made the wrong turn so I made a U-turn and halfway through the turn my car slowed. The radio turned off and i was coasting with no power forcing my steering wheel to turn so I could pull over to the side before it came to a complete stop. I immediately tried to start my car while gassing it at the same time and it just cranked. I opened up the hood and noticed a lot of build-up around both terminals of the battery.

I jump started it. Nothing.
I bought a new battery. Nothing.
Replaced the terminal and battery cables. Nothing.
Checked the purge solenoid valve. It was still good.

Could be the alternator or my timing belt. I have no idea.

This isn't the first time it died. But it was the first time that i couldnt get it started after it died.

Out of all the times it died, I noticed one thing in common...It died whenever I was making a left turn.

First time it happened, I just got it back from the shop for fixing my brake light. I drove for a good 2 miles then when I merged to the left lane it lost power and slowed. It started up right after.
Second, it was during a left turn at an intersection. Took a while to start it but it went and it was a jerky ride for a short distance.
Third, it died as I was parallel parking. I was turning my wheel a whole lot, then my wheel got stuck and power died. I started it up again with no problem.

At times my steering wheel would make a metal knocking sound whenever i turned it and it got progressively worse to the point where it was always making that sound.

Also, whenever i filled up gas. It's hard to start. I have to gas it while i turn my key to get it going.

My check engine light is on for a reason i dont know.

Don't wanna take it to the shop if it is a easy diagnosis and fix. Please help!