Okay slightly less confusing explanation of what I did. You don't need a microphone to make this work. I have this free open source audio recording program called Audacity. In it you can select which source to record from in that drop down box from the top (as seen in the picture). It defaults to microphone, selecting Stereo/Mono mix makes it record from what's playing in your speakers. However instead of just just doing that, it seems to change what's being played directly into mic input in windows itself. Meaning if you leave it on Stereo/Mono Mix and close the program, put on some music and open anything else that records from the mic (teamspeak, windows sound recorder, skype) and you will notice it to will instead of grabbing mic input, grab what's being played. So if you don't have a mic, you can just leave it on Stereo Mix and any sound/music being played No$gba should think is mic input (as I said the music in Phoenix Wright 1 was good enough to blow away the fingerprint dust). Of course since mic input in No$gba only works if sound is on, you can't stop it from accepting the music as input at will (well you could probably just turn sound off for a second then turn it back on, I've no game that requires that to try it out on). This of course probably will make your mic useless, however simply setting the drop-down box in Audacity back to Microphone should make it work again in Windows. Hopefully that helps. Apparently Hiei-YYH and sigmax got this to work so hopefully it'll work for others.
Super Simple explanation minus the reasoning or observations above. Get Audacity, select stereo mix in the drop down box as pictured. Close the program. No$gba will now pick up sound being played as mic input, the emulator's music will have some effect, play something in an audio player for more noise.