Latitude E6540's AC Adapter slows my CPU

I have Dell Latitude E6540, 4th Gen, 2.80 Ghz CPU Core i7.

I've been using it for 2 years, at the beginning I used to work with the laptop with the ac adapter plugged-in and without the battery. and It was working very well.

When the battery is not plugged in the CPU is so slow like it goes to 0.30 Ghz, and the laptops turns to be so slow and lagging too much, but once I put the battery on, the CPU speed goes right away to it's normal range.

also now, when I try to turn on the laptop with the battery plugged in, after the Windows icon, the screens goes like as in the image bellow:

Then after a while it turns off by Itself

There's also this Error message that pops out every time i turn the laptop on

These are the AC Adapter and the Battery i'm using:

Battery Image - Click Here

Ac Adapter Image - Click Here

Ac Adapter Image 2 - Click Here

NOTE: The battery doesn't charge, like sometime it does, sometime it doesn't, like at the moment it's charging, but it's been plugged for days, but not charging.. Weird.

Please, I would like to figure out which one i need to change, the adapter or the battery.

Thank you.