Looking at your specs I would say it is down to an unsupported video card,
Battlefield: Bad Company™ 2 requires at least the following minimum configuration:
Operating System Windows XP (SP3), Windows Vista (SP2), Windows 7
Processor Pentium D, 3.0GHz / Core 2 Duo, 2.0GHz / Athlon 64 X2
Memory 2GB RAM
Video Card Video card must be 256MB or more and contain these chipsets or better: NVIDIA GeForce 7800 GT ; ATI X1900. Laptop versions of these chipsets may work but are not supported. Updates to your video and sound card drivers may be required.
HDD Space 15GB for Digital Download Version, 10GB for Disc Version
DVD Drive 8x DVD Drive or greater
Soundcard Soundcard with DirectX 9.0c compatibility
DirectX DirectX 9.0c
which if that is the case, the only real solution is a new card. Even if you could get the game to run on that X800, it would be on all low settings and at a low resolution.