MoM, all motherboards have a model number, and serial number, even the ones in a prebuilt machine.
But information on those boards tends to be highly limited.
@nline, I suggest poping the cover off of your case, and looking at the motherboard for anything printed on it in large text, that tends to be the model of your board. You can also try cpu-z from CPUID - System & hardware benchmark, monitoring, reporting
and click on the motherboard tab and see if it lists a model.
Also, this deals with hardware, not software @nline. :-p