I have 4 convectors in my condo, and all of them have some water damage on the left side. I don't know where the water is coming from. There's an outlet next to each one and the damage is around them, so it may be coming through there. Someone told me that the insulation may have come off (I think the units may be the original ones which would make them ~40 years old). There's concrete there so I can't go straight through to get to the pipes in the wall. Any ideas/suggestions?

I've attached pix of the damage, the whole unit, and 2 close-ups of where the pipe comes into the unit.