Yes, I have help. Thing is you are trying to fly to a wrong planet core. Meaning the planet where you appear isnt the planet which core you should close. There is another planet there in the distance that is destroyed and has a melted core there. You open your map and look far far away then set course to it.
The Doomsday Device is a painfully slow mission if you attempt to solo it. All around the rind of asteroids are clusters of cannons in 2's and 3's, sometimes with a Klingon Battleship too. It forces the player to fly slow and even stop and kill one cannon at a time or face total destruction. As an escort ship, I had a lot of difficulty with this. Then finnally came the Doomsday Device. It was kinda cool actually once I figured out that that broken planet was the one mentioned. So I encountered the Doomsday device.. it reminds me a lot of the Death Star. So you have to wait until it fires it's massive blast of energy before you shoot it with one of your torpedos (which load into the equipment slots by the way). One major bug though, it will only target players and not NPC's. I died like 4 times to that dang thing before I got it down. The only thing I can suggest if you have not done it yet is to be as far as possible from it when fires, but someone has to take a hit.. it takes about 4 missiles to kill it. If you have a cruiser, use it to tank.. and charge the shields facing the device. Other than that, good luck.