Giga-Byte motherboard is not working properly with a memory of 4GB

Let me venture a guess - you're running a 32 bit (x86) operating system, right? Thirty two bit OS can only address 4GB of physical addresses; some of your hardware (most notably, your video card[s]) needs to 'memory map' an access area for the OS to communicate with the hardware; an area thus 'mapped' cannot also be used for storage by the OS, as it's physical addresses are excluded - thus the 3.4 GB 'visible' inside the OS; moving to a 64 bit OS, such as Vista x64, or Windows7x64 will 'cure' this problem - my OS 'sees' the whole installed 8GB...

If your BIOS sees the whole 4 GB of RAM (I am pretty sure it does), you do not have a hardware problem.

I will research further; that is an old motherboard - a whole generation of motherboards were limited to thirty-two physical address lines from their CPUs, which has the same effect as the 32 bit windows problem; there are still devices that operate through 'mapped' memory; but, in this case, the actual mapping is done in hardware, rather than in software, as is the windows case... Unfortunately, the results are the same - you will only 'see' some incremental amount less than is physically present in your board. These boards typically will not accept more than 4GB of RAM, and will not benefit from a 64 bit OS, as the devices cannot simply be 're-mapped' in software, as the actual physical locations are 'used up'!