Find a black/yellow wire coming out of the power pack and disconnect that. Also a model # would help.
with key off the black and yellow wire is short to ground and with the key on the wire is open not short to ground so the switch sounds to be ok
You could start right here on I-Boats and go from there.
You can find the parts you need at this site
1999 Johnson J35PL3EEM 35 hp Outboard Motor Parts
If the oil injection system hasn't been removed I highly recomend you get rid off it.