Precision M6700 Power Issue

Okay, so this has been a long-running problem that has just been getting worse and worse.... To start with, my laptop has always experienced a severe drop in performance when the AC adapter is not plugged in. When running only on battery power, it struggles to play HD video, run multiple programs at once, and even hold WiFi connectivity. I tested this by playing an HD video with the AC adapter plugged in, then pulling the plug while it was playing. The frame rate INSTANTLY dropped to about 4 FPS, then INSTANTLY recovered as soon as I plugged it back in. Essentially, the laptop is unable to supply itself with enough power to do anything but its most basic functions. For a long time, this wasn't a big deal. I almost always had my laptop plugged in anyway, and carrying the charger around wasn't that big of a deal. Then, the second problem started. About 90% of the time when I plug my AC adapter in, I will get an error message saying (approximately) "AC adapter not recognized. Please insert Dell approved AC Adapter." It is a Dell approved AC adapter, it's the one that came with the computer! When this error message pops up, the battery status is listed as "plugged in, not charging". However, sometimes (but rarely) even though this message is displayed, the battery DOES charge, just slower than it should. Regardless, whenever this error message comes up, I experience the severe performance issues stated above. I have replaced my battery and my AC adapter several times. I said above that this happens 90% of the time. Seemingly at random, this error message will not pop up, and the computer will charge and function as normal. An example, to give you a sense of how random it can be: I'll be sitting with the computer in my lap, plugged in, functioning fine. I will shift in my seat, and the AC adapter will fall out. I will IMMEDIATELY plug it back in, same outlet and everything, only to receive the error message and lose functionality. Even this was workable for a while. I would repeatedly plug and unplug everything, restarting my computer over and over until it finally decided to recognize my adapter, then I would just be very careful not to unplug it until I absolutely had to. This brings me, however, to my third problem, the one that has made my laptop unusable. While in the middle of this process of unplugging, restarting, etc, my whole computer screen began to flash, almost like a strobe light, on and off. This is not an occasional annoyance, it is constant, and fast. This begins to happen after I login to my account. I have to believe that this is one underlying problem, and my gut (plus months of experimentation) make me think that it's some simple hardware problem. The problem is, I have no idea what specifically I should be fixing/replacing. Any thoughts?