are the slingshot switches too close?

Locked on at power up means a short in the circuit, probably at the board. Do not play the game or leave it on more than a couple seconds at a time.

I don't think a switch closed will cause this. First, you would have to start a game to have the switch trigger the coil. Second, even if you hold the sling switch in, the coil pulses and releases. No, it's not the switch.

Tron and spiderman may use the same power board if you wanted to swap them to test. Otherwise, get the manual out and find the coil in the coil chart. Or turn in the game and open the coin door to discharge the locked on coil. Go to the diags menu the coil test. Step through to the coil for the sling. The coil number will match up to the board transistor. So coil 6 would be Q6 on the board. Then follow the pinwiki steps for testing a shorted transistor and replacing it.

Edit: if game is under warranty then call stern. They'll send you a replacement power board or have your distributor do it.

On my TF-LE the transistor for the left flipper shorted within a week causing the coil to lock on (and blow a fuse). I wouldn't be surprised if that's the case here.