Replacement MOBO for Emachines et 1331g

I Do not want to buy a new computer, no trolling that please.
I have given up hope on getting a new graphics card in hopes getting one that can run openGL 3.3 or better.
i do not want a new machine. I'm hoping that if i get a new motherboard it'll have some inter graded graphics that would have open gl 3.3 or better to run. It's for gaming. So is there a mobo i can put in this machine that would be compatible, just want open GL and it to be for windows 7. Oh wise internet wizards, is there hope?

I got some current upgrades for my machine, if they are not compatible I can replace them, just letting you all know so mabye it can help:

got a new power suply, I installed it, it's in there running great, right now. works perfectly.

http://www.ebay.com/itm/New-PC-Power-Supply-Upgrade-for...

Here's what the inside of my machine looks like right now:

https://photos.shutterfly.com/gallery/17255bfb-35f7-4a0...

Here are the system specs:
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 eMachines
System Model ET1330
System Type x64-based PC
Processor AMD Athlon(tm) II X2 235e Processor, 2700 Mhz, 2 Core(s), 2 Logical Processor(s)
BIOS Version/Date AMI P01-A0, 8/13/2009
SMBIOS Version 2.6
Windows Directory C:\Windows
System Directory C:\Windows\system32
Boot Device \Device\HarddiskVolume2
Hardware Abstraction Layer Version = "6.1.7601.17514"
Installed Physical Memory (RAM) 6.00 GB
Total Physical Memory 5.75 GB
Available Physical Memory 2.62 GB
Total Virtual Memory 14.7 GB
Available Virtual Memory 10.7 GB
Page File Space 9.00 GB
Your solution


Here are more specs just in case:
Operating System
Windows 7 Home Premium 64-bit SP1
CPU
AMD Athlon II X2 235 31 °C
Regor 45nm Technology
RAM
4.00GB Dual-Channel DDR2 @ 401MHz (6-6-6-18)
Motherboard
eMachines MCP61PM-GM (CPU 1) 41 °C
Graphics
L1932TQ (1280x1024@60Hz)
256MB NVIDIA GeForce 6150SE nForce 430 (Acer Incorporated [ALI])
Storage
698GB Seagate ST375052 8AS SCSI Disk Device (SATA) 41 °C
298GB Seagate ST332041 8AS SCSI Disk Device (SATA) 40 °C
Optical Drives
HL-DT-ST DVDRAM GH40F SCSI CdRom Device
MagicISO Virtual DVD-ROM0000
Audio
Realtek High Definition Audio

 

Nevermind about the graphics card, the pci-e slot snapped. there's no way a graphics card could stay in there all way. Anyone got any motherboard sugesstions I can put in into the machine? Preferably with some kind of graphics that has open gl 3.3 or better on it? I need it to play fallout 4. This motherboard is a broken dinosuar.