2002 diff failing???????

How can I tell if my front diff is going. I have a 2002 1500HD 4x4 with a 6lt engine. I have a pretty loud hum coming from the front end. The truck has 340000kms on it, so it is coming time to replace/repair some things here. I have so far eliminated u-joints, cv axles, wheel bearings, t-case(just rebuilt), rear diff(just rebuilt last year). It really sounds like the truck is in 4x4 when it is really in 2wd going down the blacktop, but it does not fight itself when turning either. What do you think????? Can anyone give me some ideas on this. Thanks.
Jay