So the PS2 keyboard did not work? I misunderstood what you meant there. When did you plug in the PS2 keyboard to try that? Because it must be plugged in before the computer is turned on.
Do you have a DVD player in the computer? If you can could burn a DVD from another computer with your drivers on it.
Or if you have network connectivity you can download them to the hard drive but you must be able to type.
In fact getting to Windows Update may actually offer the needed driver but again you need to be able to use a keyboard. Please try the PS2 keyboard again, making sure the computer is turned off when you attach it.