Make sure after you've completed building it, you talk to the "Engineer" for whichever faction you've decided to side with.
They'll tell you when it's ready for you to go.
Once that happens, you just need to step onto the pad in the middle.
Also, make sure you've built it correctly.
Even though you build 4 separate items, you end up with only 3 in the end since you need to snap the large tripod onto the smaller triangular base, with the Control panel and Dish off to the sides. All connected to the same power grid. (Not sure if it's necessary or not but I wired them all to each other as well.)
[Edited by Raalgra, 12/2/2015 8:09:45 PM]
Having the same problem with this quest here.
Some people have acted a bit superstitiously with this quest claiming you must do things in a particular order, but before now I've thrown the teleporter together in any order with 30+ power and it just worked (regardless of factions, etc). It appears that since the 1.3 patch went on, the quest no longer triggers correctly (i.e. when your scientist tells you to step on the platform). It's as if the game no longer realises the teleporter is "powered up" (which it is, you can tell by the noise and sparks coming out of it!)
So, unfortunately it looks like a new bug introduced in 1.3.
Does anyone have a list of the setstage commands for this quest? I can't find them anywhere. At least then people could continue their games (on PC, anyway)