I don't think you have any options other then not using that keyboard. If what I think is happening is actually happening, then the software divers for that keyboard are needed before the computer will know that anything is being typed. Can you get into the system BIOS with that keyboard? That at least would then prove if the divers are needed or not, because they will not have been loaded at the memory check stage yet either.
There might be some real good wireless keyboards that have built in hardware to decipher and translate the signals that it is recieving from the keyboard in hardware that is attached to the computer and then send to cooresponding keyboard interupt code to the computer, but I do not think it is really a needed option in the eyes of most product designers who are focusing on lowering production costs and thus overall product cost to the consumer so that he/she will buy their product instead of someone elses. The problem that you are faced with is the only type of situation where the system will not have the ability to use the software drivers they have written to properly deal with keyboard strokes.
Like I said, try and get into your BIOS at the memory check, and if your keyboard works there fine, then what I have written above is not the cause of your problem and it is something else. But, if you can't get into you BIOS at the memory check with your keyboard, then you will know that no keyboard strokes are recognised untill the keyboard drivers are loaded and this is what is causing your problem.