Bank of America does not recognize my computer?

Hi,
I have a problem and was hoping for some good advice. Our company has several bank accounts with Bank of America, and 2 workers on 2 totally different computers not linked together, in 2 separate locations, both encountered a strange message when they tried to log into the bank accts. at Bank of America yesterday morning.
I don't have the exact wording, but when they clicked their normal link that brought up BofA, they got a message stating BofA did not recognize their computer (no their cookies had not been recently deleted) and that they needed to verify the computer by giving out the debit card #, pin, and the security code on the back, or that you could verify the computer by putting in the taxID of the business, or Social Security#.
One employee did not enter in any information and called tech support. They said her computer was locked and gave her a special code to get into BofA. However, when using her normal shortcut she still could not get past that screen. She went to google, got to BofA from there and was able to log into the account.
The other employee did give out the Taxpayer ID but still could not get in, until the other employee told her to get to BofA through google, and use the new password she had gotten after getting into the account.
Then we get a call from BofA fraud, saying we have a virus on our computers and to call them. We called and they said we have to change all of our bank accounts because their computers were showing we had a virus that copies keystrokes and our accounts were compromised.
How could 2 computers in 2 different locations encounter the same problem when logging into BofA? Could the virus be on BofA website? One of our computers does have anti-virus software, I don't know which one.
Thank you for your time.