Welcome to the forum. Love the thread title.
First, how was it determined there is a blockage in the skimmer line? I may be wrong but any pool chemicals dumped into the skimmer should dissolve relatively quickly if they somehow managed to plug the line in the first place. I dump all kinds of stuff in mine, with the pump running, and never had a problem. Some questions:
-- Is the pump priming and trying to suck water? i.e. is the pump basket chamber filled with water or dry?
-- If it isn't primed, have you tried filling the pump basket with water and turning on the pump to see if it tries to pump?
-- If it is primed, filled with water, and there really is a blockage, the pump will be making some strange noises as it's trying to pull a high vacuum. Hear any loud strange noises?
Post again and we'll work further.
Al