That doesn't make sense. If your mic is going into the keyboard and the output of the keyboard is going into the Bose then it should all be reproduced.
Are you are losing part of the signal along the way? Could you be getting only the one side of the kb output and the mic is panned to the other side? Or is the mixer panned too far one way?
You should be able to run stereo out from left and right from the PA900 into the RCA stereo inputs on the Compact and get great sound. I have done exactly that with no problems.
If you aren't then it's either the cables or something is wrong with the Bose.
If you're getting the full sound but hearing noise, then it's most likely some bad cables somewhere along the line, either from the kb to mixer, or mixer to Bose. I never turn the Compact volume (input actually) past about one o'clock. Check the levels from kb to mixer and output of mixer to see if they are fairly hot but not overdriven.
If all this doesn't get results, call Bose. They are wonderful about helping you while on the phone. They will walk you through your setup.