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I remember playing a game years ago that was sort of like a cross between The Incredible Machine and LabVIEW. Instead of placing physical parts, you placed pieces of a circuit, which would allow information to flow between those pieces, including not just on/off signals but also numbers and sounds. The game had a bunch of puzzles, and there was also a sandbox that let you design your own circuits from scratch.
That's probably enough to get an exact match given that it's the only game like it I've ever seen, but in case some additional memory jogging is needed, since I remember pretty much everything about the game besides the name:
There were a whole bunch of pieces that allowed a player to interact during runtime, including a plunger, a counter, and a button that could be mapped to the keyboard. Sounds could be generated through a part that could be set to several animals, including cows and dogs. There were a bunch of pieces to do arithmatic and logical operations. There were at least two types of text displays, one which just displayed a message on recieving a positive signal, and one that mapped numerical input to various messages. One piece, which looked like a train track, let you switch between two different inputs. One of the puzzles was a safe that hid all of the logic and made you guess at which buttons you needed to press, and another required you to rig up a bunch of buttons and spam them before a timer ran out, or just cheese it by not hooking up the timer in the first place.