If you want to settle the Prime Directive problem, here's a suggestion :
The asteroid's systems are indeed starting to deteriorate, but not too severely. However, this is enough to alter the sensor's reading of the PC's ship, who should then detect a vast technobabble field on the asteroid (the asteroid hull could shield the lifesigns aboard from the sensors).
Hence, while trying to study or even correct the technobabble thingy, they would unknowingly make the matter worse for the asteroid people...
I have however no suggestion right now about the technobabble problem.
"The main difference between Trekkies and Manchester United fans is that Trekkies never trashed a train carriage. So why are the Trekkies the social outcasts?"
Terry Pratchett