An interesting problem .... It does suggest that the power supply has taken to generating a spurious signal which is swamping the desired signal from the router/modem however .....
However suggested earlier tests will soon confirm or eliminate that.
It can be helpful to have something like Net Stumbler
NetStumbler.com available - ideally on a laptop - to see what's going on in the immediate area. This won't identify the possibility above, but will let you see what channels the other networks in the area are using. Given the popularity of the 'net, it would be surprising if there weren't a few accidental clashes of 'same channel' in some situations.
Caution: You may find that some neighbors use very interesting names for their network SSID. I won't expand on a few that I have seen around here
Good luck,
FORudder