okay, after you go to the radio tower and killed all those freaky team rockets, you should be able to go to blackthorn city from mahogany town because now that ragecandybar dude will let you cross.
You have to defeat Pryce and solve the Lake of Rage mystery in Mahogany Town. Then, travel east of Mahogany Town to go through the Ice Path, which leads directly to Blackthorn City.
you have to have all 7 badges and go on to mahogany town if you met lance(meet him at the lake of rage) and enter the house next to a weird looking tree beat team rocket and go to ice cave (pass the...
well i dont exactly know but that guy who doesnt let you through says you have to visit the light house and pharmacy either they are at olivine cianwood. SORRY i didnt know