I can sum this one up in one word, Crap.
Unbelievable story line, no good actors, and the character's traits were stressed too much. And most of the main characters die.
The core of the earth stops spinning which causes problems with the earths electrical and magnetic fields or whatever. Huge electric storms begin popping up all over earth, the biggest of which hits Rome (terrible scene). Aparently electricity pools in stadiums and when enough is collected the entire stadium will blow up... A select group of people are sent to the core of the planet in their ship in an attempt to restsrt the core with a bunch of nukes. They encounter radically fictional obstacles, including the inside of a geode that was floating around in the mantle, and diamonds the size of a city. Upon reaching the core they realize that its density is much less than they expected and because of it, the nukes they brought with them werent going to be strong enough to restart the core. Then the whole DESTINI project comes in... well I wont ruin it for you. The only good scene is the one with the birds towards the begining. If you see this movie, see it for the bird scene.

Phil gives The Core 2 stars (for the birds):