This is the way I read it if I missunderstood your post then just disreguard.
It sounds like you can use the dial up modem in your computer with out any problems as long as you don't have the AC adaptor plugged in at the same time. If you plug it in there get to be static on the line and you can't dial up, but as soon as you unplug it everything goes back to normal.
Assuming that it worked before the only think I can think of is there something wierd is going on with your charger going on that it is now producing that much noise on the phone line when plugged into power. Sometimes that can be a problem with the AC adaptor or somethimes it would be the charger interface in the computer. Which would mean new mobo for the laptop if you were looking to get it fix.
Again though this is only a guess. Not an expert with laptops or anything like that just heard of similar problems, and as the others said not totally sure what you meant in your post. Just throwing out the only thing I can think of.