I have a 3000 series with a 68EC030 on an SE ROM, but I think I shorted out the logic board when I tried replacing the failing hard drive years ago (it won't go past the initial kangaroo logo power-up screen). It's still in pieces in a box in my shed. Yours looks a lot like the one I have, except in one piece.
The little wavy icon is the AC symbol. I don't remember if it's a multi-color LED or not. You may want to try a new power adapter. Many power adapters are exactly the same across manufacturers: I've had Digital, IBM, Gateway, HP, Toshiba and Fujitsu notebooks run from the same OEM adapter before. Of course, I checked the ratings and polarity before I tried anything, but I was surprised how many of them took the same thing.
Anyway, mine would turn on just by mashing one of the keys on the keyboard. I don't remember any switches or anything, and it worked regardless of the battery.
The processor, ROM SIMM, and RAM were mounted on a card in mine, accessible by removing a cover on the rear. If yours is the same, you might want to check to make sure you've got a card properly seated with its ROMs and everything.