or the remote?!..do you have a remote for it.
try taking the batteries out of the pad/remote for a bit,might be a broken contact.
and if it was a neighbour,you could be looking at possibly up to about 30ft..thats the most distance ive gotten my machine to work wirelessly..out in the garden speaking to a neighbour,and had someone on voice chat too.could see through the window that the LIVE button still did stuff on screen.
either that,or one of the remotes you have in the house,has a frequency close to whats needed to switch the console on.
I had this happen when my second pad (which wasn't used much) ended up under a pile of papers during tidying with the guide button pressed. It took me a good few minutes of head scratching to work out what was going on.
If that's not right then I'd try removing all the batteries then replacing them or resyncing everything. Neighbours shouldn't be able to turn on your 360 unless by some fluke you synced them up at the same time. Makes me wonder if a big xbox 360 lan might get into carnage!