We were trying to get a dryer for my elderly aunt. A friend bought one at a yard sale and was told it needed a drum seal. My husband, went on line and followed the directions to replace the drum seal. The dryer runs for 7 minutes and then shuts off and cannot be started again for 30 minutes. Is it possilbe that we didn't repair the drum seal correctly, or is this likely a different problem?

Its more then likely over heating it might be a faulty motor the coil inside of it when it get hot it shuts off I would check the belt on it if not change the motor out

Some driers will do that when the lint builds up like concrete on the inside of the air ducts if they have a self-resetting safety. You need to totally tear it down and scrape out and wash all of the parts except the motor, which you vacuum out. Halfway doing it will not work. You can go to YouTube to see videos on how to take it apart, but do a very good job or it will fail again quickly. I would get a new belt and change it while you have it apart and get some white lithium grease and grease any bearings you find. You need to clean out a drier every two years, at least, according to the manual. You just unplug the wires from the sensors and remove ductwork that they are attached on and clean the entire thing with soap and water. Make sure you go all through the dryer and get all parts like the blower fan and housing, vacuum out motor well and clean exhaust. Mark all wires you unplug so you know where they go. Make sure to clean around all of the sensors, too. See: Dryer vent cleaning prevents fires - YouTube and: Cleaning out a dryer with top lint cleanout - YouTube
Cleaning out a dryer: By a woman 2 of 2 - YouTube
Look at these, too: https://dl.dropbox.com/u/8010163/Whirlpool%20Dryers.zip