My MacBook Pro early 2011 after a time running make slow?

Your issue is the lack of battery! Your system was not designed to run without it. Within the battery there are sensors that the system's SMC services needs access to. As you severed access your system is running in CPU Safe Mode which SMC pushes the Fans and lowers the CPU's clocking to make sure the CPU is not damaged. Without the battery the system will also lower its processing even lower when the process load is to great for running on the charger alone which you are also seeing.

As an example here's a damaged chip which would be the end of your system!

So get a replacement battery MacBook Pro 15" Unibody (Early 2011-Mid 2012) Battery

You talk about fixing your graphics chip what did you do?

@msh666 - Sadly, the GPU chip's failure is not the bad solder to the logic board its the Tin solder used to connect the silicon chip to the base within the flip chip design used in this AMD GPU series.

Here we encounter Tin Whiskers Pure Tin solder can encounter this as well as some alloys of Tin solder as well. Your resoldering (reballing) allowed the whiskers to recede enough to allow the chip to work.

So I assume you disabled the AMD GPU which is about all you can do. But! Keep in mind the Intel HD Graphics 3000 is not very powerful so don't expect high performance graphics.