MacBook A1181 when starts the screen is dimming - no inverter

I got a used macbook A1181 2006 Core Duo 1.83 Ghz (32bit- non Estar) and there was a problem, at the begging, on the battery charging issue. I opened the macbook and I found a wrong battery connector / sleep SW component. To be clear:

My logic board supports this (Non Estar- 20pins): MacBook Battery Connector/Sleep Sensor (non-Energy Star)

I found this (18pins): MacBook Battery Connector/Sleep Sensor (Energy Star)

The problem was that, when I insert a battery (original or not) the screen was dimming while (for example) surfing on the internet. So the macbook had not battery support - only by the cable.

I supposed adding the 2 missing pins manually could solve my problem.

After of many tries of adding 2 more pins and many SMC and PRAM resets, my screen dims (like inverter's problem) when macbook starts.

The only way to open properly without dimming screen is when I reset SMC and start the macbook - and fan is go like crazy!!! (that's meaning not inverter's issue)

After that I thought to clean all contacts with isopropyl alcohol in any case.

I'm trying to find the problem that I caused and I believe that if:

1. it's a software issue: is about SMC resets etc

2. it's a hardware issue: is logic board power issue

P.S. I also give you some photos from (a) the logic board (b) battery / sleep sensor and (c) a video by laptop's behavior:

https://www.dropbox.com/sh/0spkzmkjetys4...

Thank you in advance and sorry for my English.