You have the battery, charger and the mainboard.
What many don't realize is the battery is 300 cycle rated so if a person ran the machine on battery they could exceed its rating in one year. You have a machine that is years old so the battery is suspect. I'd start with a new battery first then a new charger. If it's the mainboard get estimates.
But if it's not saying plugged in, in your case I'd try a new charger first.
ok I've had this problem for a few months now, about once a month I'll be on my laptop and and it'll go into power saving mode (dimmer screen, keyboard lights turn off, etc.) like when my laptop isn't plugged in. On the battery icon it's also reading that it isn't plugged in. So, to fix this I turn off my laptop, unplug the battery, and hold down the power button for 30 seconds, then plug everything back in. This works and everything goes back to normal for about 3-4 weeks then I have to do it all over again. My question; is there a way to fix from having to do this every few weeks? Is it a problem with my chord? Battery? or, am I doomed to repeat this until my laptop eventually dies?
My laptop is an Alienware 17, brought brand new in Oct. of 2013. It's running 64-bit Windows 7 Ultimate. it has an Intel Core i7-4800MQ @ 2.7GHz. If you need any more info please let me know.
Any help would be greatly appreciated thanks.

Chowhound
Comic Vine
GameFAQs
GameSpot
Giant Bomb
TechRepublic