short problem?

Hi mates, it's been a while, let me tell you i think my 7g's got a electrical problem, when you turn the lights on, the check engine light comes on and the engine tends to shut off,or when i use the brakes,the lights start to dim.
The battery it's ok,brand new and the alternator charge 14 volt at low idle even with lights on.

Battery it's 12,7 volts

Other synthom is when i turned off the engine i use the alarm and it sounds like the battery is very weak,then i try to start the engine and just hear a little click, it's like a dead battery but with a new battery and then the alarm start to sound and the led alarm start to light very quickly.

I checked the - terminal to chassis and it's ok,

what can i do, i don't know what else to do, any ideas?

thanks mates

hey thats pretty much exactly what happend to me. What I did was replaced the battery and it didn't fix the problem... so I got a new alternater, and it fixed it completly.... but you said your alternatiors giving you good power at idle with the lights on... So I don't know exactly what it could be.