Hmm, I'll not get into details of the wiring method. Looks like u are using two singlecoils (since ur humbucker is broken, so, for me at least, there's no need of connecting him if it doesn't work). I have a guitar (that I made myself) with two singlecoils, wich I connected in parallel mode. I have some "hiss" on the background. You hum may be causing because of one of these:
1. the hum gets louder when you touch the bridge or the strings? If yes, then take of the wire that leads to the bridge, just cut it off on the middle of the way
2. the hum is there (and loud) touching or not the bridge? Then check the wiring.
3. the hum is very low and dissapear when you touch any metal piece in contact with the volume pot? Try grounding it someway.
Hope it helps. Hey, if u get anyway of taking off the hum, send me a PM, ok . c ya!