Power supply issue

I have a Lenovo IdeaPad n586. Got it a bit over a year ago, and for the past few months I've been having an issue with (at least from what I can tell) the power. Currently, I use this laptop mostly for gaming, as well as using it for random art ideas. For the past few months, I've had an issue whenever I start playing a game. I'll start up something (for example Team Fortress 2) and for about 5 to ten minutes everything will work fine. Then the batter light will turn orange and flash, with the power light remaining on. after that, the battery will not accept charge, but the computer will continue to work. It will only accept charge when the computer is in sleep mode or turned off. The problem seems to persist when I restart my computer, but after waiting for some time (I usually wait an hour or two) it seems to work fine again. When I take the battery out, it's a similar situation but instead of the lights flashing, the computer simply turns off entirely. Now, I don't know the specific problem or what caused it, but here's what I've found so far:
-The battery and adapter work fine, there doesn't seem to be any problem with them.
-All my drivers are up to date.
-I haven't had any blue screens or major software issues.

That's about all I've got really. I'd really like to avoid getting a new computer, so if there's a way to fix this that you know of or can dig up, please let me know. Thanks for your time, and anything you've got is greatly appreciated.

Here's my computer's specs, just in case it helps

OS Name Microsoft Windows 7 Home Premium
Version 6.1.7601 Service Pack 1 Build 7601
Other OS Description Not Available
OS Manufacturer Microsoft Corporation
System Manufacturer LENOVO
System Model Lenovo IdeaPad N586
System Type x64-based PC
Processor AMD A6-4400M APU with Radeon(tm) HD Graphics, 2700 Mhz, 2 Core(s), 2 Logical Processor(s)
BIOS Version/Date LENOVO 68CN17WW(V1.03), 4/19/2012
SMBIOS Version 2.7
Windows Directory C:\Windows
System Directory C:\Windows\system32
Boot Device \Device\HarddiskVolume1
Locale United States
Hardware Abstraction Layer Version = "6.1.7601.17514"
Installed Physical Memory (RAM) 4.00 GB
Total Physical Memory 3.48 GB
Available Physical Memory 1.30 GB
Total Virtual Memory 6.95 GB
Available Virtual Memory 4.14 GB
Page File Space 3.48 GB
Page File C:\pagefile.sys