The Enterprise didn't even need to fly to the edge of the Briar Patch. They could've just send a shuttle that made the distress call. It doesn't seem likely that they spent months in the Briar Patch or something - that was likely a matter of days.
As Tumerboy said, I can only imagine that Starfleet got a couple of spare warp cores lying around. Those kinds of things must happen rather often with a fleet that big (and exploration-savvy).
Wait why would you want to do that? It's good to know what side of a ship is weakest!
Because it is ugly?
Also, I don't have time to look at the space-area of the screen during combat... My focus is on the HUD during combat... (minimap, enemy indicators on the border of the screen, skill tray, ship status thinge (wich also shows how much shield you have).
Yeah... I figured it would be something like that... but whenever I think about La Forge ejecting the warp core in Insurrection, I just wanna scream "Hey, what a great idea! Eject the warp core to keep the ship from being destroyed! What, did you read the Engineering 101 manual after Generations?"
He wasn't thinking straight. He was captured and tortured then when he got back to the Enterprise they removed the nano probe and sent him back to work on the same day .... :p
Starfleet could also send out the Corps of Engineers, with a replacement warp drive, or even a temporary "spare tire" warp drive for such a ship.
It may take a couple of weeks to get into place and hooked up, but that beats the decades or centuries of limping along at impulse.
OF they could have a spare warp core in cold storage like Voyager did. The MSD display show a second warp core in the secondary hull. According to Dub Drexler the secondary warp core was in cold storage. It would have to be unloaded loaded, assembled and installed on the ship in 2 weeks, IIRC.