BIOS Virus Question

No, I'm not asking how to write one, what I'm asking are some details as to the suseptibility to them. Here's the situation (and please let me know if there's a better catagory then this one for this thread).

I have 2 computers at home. One of them I keep my business information on (computer a.) and it is also completely isolated from the internet. I have another computer (computer b.) that is connected to the internet, both computers run antivirus software. Now and then I may have the need network my internet computer and my unconnected computer via an ethernet connection. The data on my unconnected computer is very sensitive. And yes, the medium has to be ethernet connectivity between the two.

Here's my question. If I take computer (b) and remove the hard drive with the current OS/info on it, and replace it with a "clean" hard drive, one that's never been connected to the internet (so ofcourse I'd disconnect my internet connection to computer (b)) and running a clean OS on it. Can I then connect the two computers together (computer A and computer B [with the clean HD]) and not worry about potential viruses. Or is it possible that someone (i don't care who) could slip me a virus that somehow runs in the BIOS or in the RAM which is then passed to the clean HD on computer B and then passed via ethernet to computer A? . I'm mainling thinking about a passphrase capturing virus.

Is this anything to worry about, or does anyone know where I can find out. I know it sounds paranoid, but I"m talking super sensitive (legal) data which could financially make or break me.

Any help would be awesome. Thanks everyone.

Unless I am confused the new hard drive in system b poses no threat greater then the one you have always taken because you state that you connect A and B together now.So the worry is gonna always be there but in my opinion with a fresh drive the risks should be less way less.......

u wont get any on your coms that would be a thret to ur pc cos there is not room the ram would bee cleen once it has been swiched off if u are real paranoid clear the coms but u should be fine with a fire wall and an upto date virus scaner any way
what u could do is put the new clean disk in to ur important pc partition the disk put on the data into one partiton then install windows or what ever on it later on to another partition and therfore never phisicly conect the pcs and u would be nearly 100% safe