Like L.Dutch - Reinstate Monica, I don't see a good reason for this population/civilization to get into space. It's not the tech that's necessarily the problem, but psychology is a huge factor when the people can't perceive something. And perception is a huge factor when trying to comprehend something.
It would have to take some very special circumstances to align just right to let this happen. For instance, in the communication or other electrical gear they invent, they may notice interference. This could be interference from the nearby star, but because they can't see it, they would attribute it to something they do understand and can comprehend, the core of the plant.
It would have to take a special kind of thinker to consider putting some kind of direction finder to figure out where the interference is coming from. Most engineers would likely just work to shield or otherwise remove/negate the interference. It would take some really severe interference for more than just a single person to look for the source. If they realize there's likely no way they can do anything to prevent the interference, they won't do anything about finding the source.
And even if they do find that the interference is "up", they probably still have a taboo about going to the surface, due to the circumstances you describe about how they became cave dwellers to begin with.
Even if the thing they discover is deadly radiation, that just plays into the taboo and they are more likely to dig deeper to get away from the radiation, rather than go towards it.
Since their ancestors chose to "run away" from the dangers of the surface, instead of invent technology to deal with it, they likely have a civilization based around this fear. It doesn't even matter if the ancestors had the resources to invent the tech, they still chose to dig down. With any civilization, there's a lot of pressure to "continue to do as the ancestors did". This is how "well we've always done it that way" comes to be as a saying, among more dangerous doctrines, but I won't get into that.
With this taboo, even if the original thinker figured out that the interference/radiation is gradually reduced then disappears completely in an area, then realizes there's nothing causing this below, so it has to be above (a lake or ocean), it would still take quite a bit to convince the people in charge to figure this out.
Then again, they may already be living there and know about the phenomenon without caring why it happens, and literally no one in generations has thought to ask why. It may have even worked into the taboo no to ask that type of question.
And with strong enough taboos, they can work into laws. It may even be against the law to go to the surface.
Maybe all this works into the story, where the original thinker decides to go off on their own to discover "up". They would likely have to work on their own for quite a while, until they secretly convince others to join the venture. It might even become a haven for the "unclean" (or whatever) who make a nuisance of themselves by breaking the taboos/laws about "up".
This is still a tenuous story line, but I've enjoyed even more unrealistic plotlines, as long as it can hook people by their emotions and/or curiosity. :-)