Long-term framerate drop from power loss

I wasn't sure how best to describe it in the title. Basically, whenever I unplug my AC adapter from my laptop, or the flow is otherwise interrupted, it powers off. It's been stuck at "0% plugged in, not charging" for years. That problem's not so hard to live with, I suspect that it arose because I keep it plugged in 24/7 anyways. The problem I've come about is that when it's unplugged, even if the power's already off, when I turn it back on, everything's slower. My framerate in games drops, my browser windows take longer to load, hell, even my desktop lags. I've had this problem for a couple years now, and it does fix itself temporarily every now and then. It'll just spontaneously work normally again, sometimes after a couple weeks, sometimes after a couple months, and I've been living with that. Every time I have to move it, or I'm careless and the cord falls out, I just wait. Anyways, what I want from you guys, is to know if you've encountered a similar issue, or perhaps know how to trigger it's spontaneous fix. I assume I already know what causes it, and it could be fixed with a simple battery replacement, but that's just not in the cards for me right now.

So... yeah. In summary, my laptop sucks for a while when I unplug the charger and I want to know how to shorten that while.

I'm no expert, so I'm not sure what you'd need to solve this, so I'll just supply some basic info about my laptop. As in, just what it says on the little plate on the bottom. More info can be supplied upon request.

DEPLOYED: March 21, 2014
Alienware 17
GeForce GTX 765M with 2GB GDDR5
Intel Core i7-4700MQ