haider95 :
Whats the processor that you are using right now? whats the motherboard model? Go into start>Run>type dxdiag> copy paste it here, then go to display tab and copy paste that too. From what i know of the GX620, it usually comes with a pentium D, having said that you can easily upgrade to a better core 2 duo but not the ones with the 1333MHz bus speed. The e7xxx/e6xxx/e5xxx/e2xxx series would make a good upgrade. Search your motherboard for a pci express slot. Im sure you know what that looks like, if it has one then tell us your price range and we'll suggest a graphics card.
System Manufacturer: Dell Inc.
System Model: OptiPlex GX620
BIOS: Phoenix ROM BIOS PLUS Version 1.10 A11
Processor: Intel(R) Pentium(R) 4 CPU 3.00GHz (2 CPUs), ~3.0GHz
Memory: 5120MB RAM
Available OS Memory: 3574MB RAM
Page File: 1420MB used, 2793MB available
Windows Dir: C:\WINDOWS
DirectX Version: DirectX 11
DX Setup Parameters: Not found
User DPI Setting: 96 DPI (100 percent)
System DPI Setting: 96 DPI (100 percent)
DWM DPI Scaling: Disabled
DxDiag Version: 6.02.9200.16384 32bit Unicode
Card name: Intel(R) 82945G Express Chipset Family (Microsoft Corporation - WDDM 1.0)
Manufacturer: Intel Corporation
Chip type: Intel(R) 82945G Express Chipset Family
DAC type: Internal
Device Type: Full Device
Device Key: Enum\PCI\VEN_8086&DEV_2772&SUBSYS_01AD1028&REV_02
Display Memory: 256 MB
Dedicated Memory: 0 MB
Shared Memory: 256 MB
Current Mode: 1440 x 900 (32 bit) (60Hz)
Monitor Name: Acer V193W
Monitor Model: V193W
Monitor Id: ACR001A
Native Mode: 1440 x 900(p) (59.887Hz)
Output Type: HD15
Driver Name: igdumd32.dll
Driver File Version: 8.14.0010.2697 (English)
Driver Version: 8.15.10.2697
DDI Version: 9Ex
Feature Levels: 9.1
Driver Model: WDDM 1.0
Graphics Preemption: DMA
Compute Preemption: DMA
Driver Attributes: Final Retail
Driver Date/Size: 10/10/2012 15:47:38, 3816392 bytes
WHQL Logo'd: Yes
WHQL Date Stamp:
Device Identifier: {D7B78E66-6432-11CF-1179-A721A3C2C535}
Vendor ID: 0x8086
Device ID: 0x2772
SubSys ID: 0x01AD1028
Revision ID: 0x0002