Agreed, you need to get a PS/2 keyboard or a USB->PS/2 adapter. I'm not sure how the adapter would work with a wireless setup though.
REPAIR installs often don't work out well for several reasons including the fact that the main problem may be a bad hard drive.
If you can't check the BIOS it has nothing to do with Windows.
I bet that your USBs are in fact working. I had problems on two different systems with wireless AND with non-wireless.
For example, on two different systems my USB keyboard would work but NOT with the mouse so I had to remove the mouse to enter BIOS (once it booted up to Windows things were fine).
Either way, you need to borrow another keyboard. Try USB, and if that doesn't work try the PS/2 slot.
Wireless setup and BIOS:
Despite there being a PS/2 connector my Logitech wireless setup would not allow me to enter BIOS. I suspect the PS/2 was only for the mouse. I don't understand why the wireless setup wouldn't work. Strange.
Other:
On two different systems, I could only boot to BIOS with my USB keyboard (had to remove the mouse) but oddly when I added some MORE USB devices things started working again (but only with the USB devices in a certain order). It sounds like a problem with the motherboard USB bus and power distribution.