The startup routine is normal. I have had the 7500 for a year or so and it is always the same. Triggers on and then about 30 seconds later the blue light comes on. Mine has always been dead silent on all fronts. Is the hum coming from your speakers or from the amp itself? If the speakers are quiet I would not make any ground connections as indicated above. Check to see if it is the amp case. There are previous threads talking about that issue but I don't know what the resolution is. Crank it up, burn it in and see if it goes away. If not Outlaw will fix it for you.
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Music system
Model 990/7500/Magnepan 1.6 QRs/Technics SL1200 MK2/Aperion S-12 Subwoofer/OWA3/Sony NS75H DVD
APC H15 Power Conditioner
TV System
Large Advent Loudspeakers/ Polk center/Monoprice surrounds/Panasonic Viera 42 inch/Onkyo HT-RC260/Sony BDP S590/Directv
Home Theater System
Onkyo PR-SC886/Outlaw 7125 Klipsch RF-82 L/R,RC-62 center, RB-35 SR/SL, BENQ HT1075, Outlaw LFM1-EX/OPPO BDP-83/Directv
Harmony ONE
Blue Jeans and Monoprice interconnects
APC H15 Power Conditioner