Currently Being ModeratedNov 7, 2013 4:30 PM (in response to Marcus111)
I would like you to ask, by "they replaced the battery connector port" you mean they replaced the MagSafe DC-In board (see the picture, the device in the right hand http://d3nevzfk7ii3be.cloudfront.net/igi/UnXMVB6e4eFgkwFY.huge) or simply said the part between the logic board and the MagSafe connector with the LED indicator, right?
I have very similar symptoms with the same MBP 13'' unibody early 2011 model. In Addition to what you mentioned, I am only able to use external (bluetooth) keyboard and mouse since the built-in keyboard does not work very well (just in the rEFInd menu, but very slowly). Moreover, I am only able to start the system when the trackpad is disconnected from the LogicBoard. The system runs very slowly by default, but if I do a little trick -- the SMC reset during which I disconnect the MagSafe, reconnect, with 5 second intervals among the steps, the system starts and runs pretty fast. The problem is that if I do it as described, the battery is not recognized in the OS X. On the top of that, as the trackpad is disconnected and keyboard does not work well I can only use external bluetooth keyboard and mouse (or USB). When the trackpad is connected, the fan starts turning but the MacBook does not start at all...just the white diode is blinking and the hardrive starts and stops spinning over and over again (like if there were not enough power).