Either your combo amp or the wall-wart power adaptor has a grounding problem, and there is a ground loop being created through the power supply when you have them all interconnected. This causes fault currents to circulate in the shields of your signal cables, and that shows up as hums in the audio. Wallwarts for audio use almost never have grounding plugs, so my bet is on the combo amp as the source of the problem.
Several possibilities exist for fixing this. First, if the combo amp has a ground switch (or sometimes a "ground lift" switch), try putting it in the opposite position of whatever setting that it is currently in. This is mostly true of guitar amps instead of more modern combo amps, so your amp may not have such a thing- but it is worth a try.
Secondly, and this is a temporary solution only: if your combo amp has a 3-pin (grounding) power plug, you can try "lifting the ground" by using a 3-pin to 2-pin adaptor at the power outlet. This leaves you with no safety ground, and as a result is definitely not for long-term use. But it can be very useful for short term fixes, such as at gigs.
Lastly, the _right_ way to fix ground loops (other than opening up the amp and/or wallwart and really locating the problem, which is beyond the scope of a quick posting) is to break the loop by inserting a transformer in the line. This positively fixes the problem by preventing the loop currents from circulating in the first place. In addition to carrying several 3-2 pin adaptors in my gig toolbox, I never leave home without at least one of these:
http://www.ebtechaudio.com/hedes.html . These are the Swiss army knife of killing hum loops at gigs: they work brilliantly, and are worth every dime. This lets everything keep its safety ground connection, and is why I advocate it most strongly. Buy one of these once, and you'll probably use it to clean up the PA at every gig you do for the rest of your career...
I have an HE2 permanently installed in the feed from my TD20/DM5/Alesis mixer back to the main board in my studio: There is an intractable problem inside the wallwart for the DM5 that I have never been able to correct. Similarly, a keyboard player I often play with has to use one between his Nord keyboard and his Peavey combo amp: somewhere there is power supply leakage that causes a hum, no matter what he has tried. Very annoying, but very fixable....
The quickie 3-2 power plug adaptor is cheap and easy, but it simply masks a deeper problem. Worth a try, though.