The blocking platform is controlled by the spade-switches *outside,* back where you last saw the quest-giver. If these switches are in the OFF position, so is the blocking platform, which lets you ride the elevator up.

But how do you get inside when these switches are OFF? You need either the action-at-a-distance upgrade, or the walljump. If you have either one of those upgrades, or both, then you can set things up such that the switches are OFF but the inside of the server is accessible.

Both of these upgrades can be found in the underground section. To open that one, toss a grenade at the cracked floor. (The grenade can be found east and up from the entrance.)