When I finished the job, and turned on HP1 to check the screen, I realised the brightness was poor (max 70% of the normal brightness) and also the 'adjust brightness' scale was decalibrated (the scale is divided into 10 steps, the first 8 steps turning the brightness up, but the last 2 turn it back lower). While doing the switch I realise I still had the battery connected on HP1. The 'transplant' is done by taking out the display with the connector from the MB, not just the lcd screen. I decide to replace the screen so I take the display from HP2 (same model, both original displays) and I install it to HP1.
Although the LCD shows signs of the accident, being partially black, the brightness of the readable part of the screen is 100%.
One day by accident I break the display of HP1. Thanks for ypur answers, and let me clarify the problem: I have 2 laptops, both are HP probook 4520s, HP1 is my good laptop and HP2 is the spare-parts laptop, both are working fine.