my connector is broken and the power cord will not go all the way in

Solution
Yep, what SayWhut says. Using your favorite search engine, look up Dell (model number here) power jack repair - that repair is common enough that companies specialize in it or, if you're the handy type (and very adept with a soldering iron - sometimes you don't even need that) there are "how to's" available. If it is the connector on the cord from the power adapter, then the adapter will need to be replaced
Yep, what SayWhut says. Using your favorite search engine, look up Dell (model number here) power jack repair - that repair is common enough that companies specialize in it or, if you're the handy type (and very adept with a soldering iron - sometimes you don't even need that) there are "how to's" available. If it is the connector on the cord from the power adapter, then the adapter will need to be replaced
 
Solution