Please help I have a strange grounding problem

I recently bought a FIM 880 outlet and installed it myself. I plugged in my amp and cdp but I'm getting a fairly loud "humming" when I play my tuner only. I don't have dedicated outlets( I'm in the process of making this my next project)so I have my tuner plugged into a Monster Cable 2000 outlet which is in another outlet on the same wall.Both outlets are on the same line as when I shut off the breaker there is no power on this wall. The strange thing is when I unplug the cdp, the hum goes away completely.It only comes back when I plug the cdp back into the same outlet as my amp. Another weird thing is when the hum is there and I get closer to my amp, the hum increases in volume as if my body is acting as an antenna. I'm not a technical guy,but it appears to me that there is some kind of a loop and by unplugging the cdp the loop is taken out. I would surely like some advice on this new and strange situation. Thanks for your help and advice.
Don't float grounds except to troubleshoot - never a good solution. With a bit of rigor, one can find the solution... When I had an issue, it took me 20+ hours to figure this out - and I am capable of performing Electrician duties... One thing to try - if you have cable, sat. or antenna, disconnect any of these connections to see if the hum goes away.. You may have a ground loop thru a antenna / cable connection.
Thanks everyone for your great suggestions. I will consider them all. Again, much appreciated. P.S. I'm not so sure now that this is a true ground hum problem after all. I usually listen only to a local college FM station that plays mainly jazz and classical.After trying without success the cheater plug on all components, I tried some other FM stations and the hum wasn't there. I then went back to my regular station and the hum was only there, so I thought maybe it's with the radio station.The strange thing is the hum decreases and increases in volume as I move toward and away from my amp. Then, while fiddling with my tuner( modified 1980's Sansui T-80 analog)I pushed the stereo button to mono and the hum disappeared completely. Then when pushing the button off and on repeatedly, the hum would come and go as well( mono=no hum,stereo=hum ). It was nice to finally eliminate the hum, but listening to mono is not my cup of tea. Any further suggestions ?
What is your antenna situation? If you improve the reception, it may solve your problem. A good attic or roof-mount directional antenna with a rotor is always a good idea.
I am using a high-end dipole called the FM Reflect from C.Crane,Inc. I think I paid around $60.00 for it.It is mounted on the wall behind the system, carefully camaflouged by bookcases so the wife will leave it there. I may go for an outdoor unit, but FM is not my main source of listening. I'm trying to figure out why I get this background hum in stereo and not in mono.
Well, I've isolated the humming problem to the FIM outlet. Apparently I didn't install it right. I am going to get an electrician in next week to put in dedicated outlets. I'm tired of sharing electricity with the rest of my house and neighborhood.I recently read a good review of an AC filter called the ISO 1100va. Can someone share their thoughts on this item ? Where can I buy one ? Thanks again for all your help in troubleshooting.