I heard you the first time, does it sound like I know what a dxdiag is? Alright im getting pissy now, sorry. I know your trying to help.
E-machine T5224
First, if you didn't understand, search or ask.
Second, when you run dxdiag on your system, look at the bottom of the first tab and click on "save all information", it will create a text file. When you open the text file all the information needed here is the stuff under "System Information", "Display Devices", and "Sound Devices".
Here is your system specs, amazing what google finds:
T5224 Support Information
Specifications
CPU : Intel® Pentium® D 820 Processor (Dual-Core)
64-bit processor with Intel® EM64T Technology
Each core operates at 2.80GHz | 2 x 1MB L2 cache | 800MHz FSB
Operating System : Genuine Windows Vista® Home Premium
Chipset : Intel® 945G DH (Viiv™)
Memory : 1024MB DDR2 dual channel (2 × 512MB), 533MHz (PC4200)
Expandable to 2GB
2 DDR2 Slots (Total) | 0 DDR2 Slot (Available)
Hard Drive : 250GB SATA II (7200rpm, 8MB cache)
Optical Drive : DVD±RW 16x Multiformat Dual-Layer Optical Drive
Up to 8.5GB with Dual-Layer Media
Write max: 16x DVD±R, 6x DVD-RW, 8x DVD+RW, 4x DVD+R DL, 40x CD-R, 24x CD-RW disks
Read max: 16x DVD-ROM, 40x CD-ROM disks
Media Reader : High-Performance 15-in-1 Digital Media Manager™
Up to 40x faster
xD-Picture Card™, CompactFlash® I (CF), CompactFlash® II, Secure Digital™ (SD), Mini Secure Digital™ (Mini SD), Multi Media Card (MMC), Reduced Size MMC (RS-MMC), MMC Mobile, MMC Plus, Memory Stick (MS), Memory Stick Duo, Memory Stick Pro®, Memory Stick Pro® Duo, SmartMedia, IBM Microdrive
Video : Intel® Graphics Media Accelerator 950
Up to 224MB of shared video memory
PCI-Express® (PCI-E x16) slot available
Sound : 6-channel (5.1) high-definition audio
Amplified Stereo Speakers (USB Powered)
Communications : 56K ITU V.92-ready fax/modem (RJ-11 port)
Intel® 10/100Mbps Ethernet LAN (RJ-45 port)
Peripherals : Premium multimedia keyboard, 2-button wheel mouse (PS/2)
Ports/Other : 6 - USB 2.0 ports (2 in front, 4 in back)
1 - VGA
1 - Parallel port
1 - Serial port
2 - PS/2 ports (keyboard and mouse)
3 - Audio (Rear): Line-in/Side (Stereo), Front/Headphone (Stereo), Microphone
2 - Audio (Front): Microphone, Front/Headphone (Stereo)
1 - RJ-45 Ethernet port
1 - RJ-11 Modem port
Dimensions : 14.50" (H) x 7.25" (W) x 16.50" (D)
Weight : 21.2 lbs. (system unit only)
Warranty : 1 Year Parts and Labor
You need a new video card to put into that PCIe x16 slot, and depending on your choice of video card the power supply is going to have to be changed as well.