If you have access to the fuse box for your apartment and if you are reasonably handy electrically, you could check to see if the grounds are even attached to the outlets. You could also try reversing the hot and neutral -- I've heard that sometimes electricians hook that up in an inconsistent way and it could cause problems. This is a long shot type of solution but only costs your time (do this only if you can turn off the power to the outlets you are checking or it could cost a lot more). Check some ground hum threads for more advice -- yes, much of it is lifting the ground (which does not work for you) or installing a dedicated line (which you can't do), but there are also other good ideas. Good luck.
Two other quick things. First, you might want to check to see if the fuse box connections are clean and secure -- if they don't appear to be, contact your landlord. Second, did you try the Creek at a friends' house to see if it might be a problem anywhere? Maybe the ground issue is in the unit (not real likely, if it sounds OK with everything else off, but it's another free test you can perform).
Two other quick things. First, you might want to check to see if the fuse box connections are clean and secure -- if they don't appear to be, contact your landlord. Second, did you try the Creek at a friends' house to see if it might be a problem anywhere? Maybe the ground issue is in the unit (not real likely, if it sounds OK with everything else off, but it's another free test you can perform).