I left my Apple Watch series 1 in the charger for weeks now it won’t turn on at all. Is the battery completely dead?

Batteries can only take so much of a charge before they are completely gone. My guess is, that's probably more than likely what happened here. It's all about how the charge cycle works, after it reaches a hundred percent, if not taken off the charger, then it will run down a little bit, maybe down to about 96 or so, and then charge all the way back up. Cycle continues until the battery either dies, or is freed from the charging mechanism.