The BIOS is a low level piece of software that will be stored in a chip on the motherboard of an IBM PC compatible computer. Firmware is just a more generic term for any low level software stored in a chip on a circuit board. BIOS stands for "Basic Input Output System" and it's basically responsible for identifying, testing and initialising all attached hardware, and finally loading the operating system (which will take over control of most of the computers functions from that point onwards).
If the BIOS is unable to identify and initialise a CPU, it may cause the PC to simply fail to start. It doesn't have the relevant information to "know" how to initialise an unknown CPU type (what voltage to apply, what speed to run it at, information about cache etc.)
As this micro PC was never offered in anything other than the processor you have there, it's doubtful to me that the manufacturers would have programmed the BIOS with information about how to deal with other processors. Enthusiast communities do sometimes create modified BIOS and firmware for various devices, to allow it to do things the manufacturer never intended (maybe like support a non-standard CPU). This relies on there being an enthusiast community with enough like minded people with the required skills to create a modified BIOS. Any installation of a modified firmware has potential to "brick" a device, and of course is not covered by any manufacturer warranty...
PS - Vista can be a struggle to run well on a full power desktop system let alone a micro PC! It's not a very efficient operating system... Perhaps you could look into running a light version of Linux instead. I used to have an old Asus EeePC which was an early micro PC, not a very powerful one. It used to run the LXDE version of 32-bit Linux Mint fine though with 512mb memory and a 8Gb SSD..
Edited by jonuk76, 22 July 2014 - 10:31 AM.