It's definitely because of your PC. Unfortunately, none of your systems specs meets the minimum requirement for black ops. Here are the minimum requirements:
PC MINIMUM System Requirements
• Operating System: Windows 7 / Vista / XP
(Any version of Vista and Windows 7 will work, 32 or 64-bit)
• Processor: Intel Core 2 Duo E6600 2.4GHz / AMD Phenom X3 8750 2.4GHz Or Better/Faster CPU
• RAM: 2 GB Or Better
• Video/Graphics Card: NVIDIA GeForce 8600GT 256 MB / ATI Radeon X1950Pro 256 MB Or Better/Faster
• Video/Graphics Card Special Requirements: Shader 3.0 Or Better AND DirectX 9.0c compatible
• Sound card: DirectX 9.0c compatible
• Minimum Free Hard Drive Space: 12 GB
(Source: http://www.cleartechinfo.com/Call-of-Duty-Black-Ops-System-Requirements-Cant-play-it-on-your-computer)
Seeing the above and comparing it with your specs:
1) Your CPU is way below the requirement and you need a better CPU
2) You are running on onboard graphics and do not have a dedicated graphics card. You need a dedicated graphics card as stated above
Even if you have the 'minimum' requirements, its not a guarantee that the game will run fine. It will be just 'playable', i.e, it will only be able to 'run'. You will need a new computer in order to play the game.
The above aside, there are many problems with games which are illegal copies/ downloaded for free/ pirated, etc. Did you buy the game or did you get it for free/ pirated?