I'm not sure which step you are on, but you could try simply leaving the system and then continuing the mission. If the mission gets screwed up, that usually fixes it.
For some missions, you might also just not be at the right planet/system to beam down to. Make sure to read the last message from the NPC you got if you can, or check your mission log and read what it says in there, if your objectives box doesn't give any more detail.
Though for the Researcher Rescue mission, I don't think you go to more than one system, which is why I suggest just try warping out and then continuing the mission from sector space. You should see a prompt to do so when you're outside the right system.
Foundry Missions: 1) The Source of Power (ST-HSWUBD5TQ) [Federation] 16+ -----=====*****<[ Fleet Recruitment Thread ]>*****=====-----