Dead short?

Are you measring the 35 ohms back into the car harness side of the ignition switch connections? If so, then the yellow wire to the car harness goes to the starter relay coil and 35 ohms seems resonable if you have an auto with it in park or neutral when you tested.

I am catching up with what has been done. Do you have a new ignition switch installed?
Have you carefully examined the wires on the ignition switch harness up into the column? Shorts there seem somewhat common.

Your prior test with the test lamp shows that the main harness to the ignition connections are free from shorts; that is good.

With the ignition connectors disconnected, and the test lamp in the battery - lead, connect a jumper between the ignition harness connectors on the black lead only. This will put 'juice' to the ignition switch but nothing out. Check to see if your test lamp glows. If yes, then the ignition switch input or wire is shorted. If not, then turn the key to all positions to see if the light glows indicating a short in the switch when in certian positions or to an output wire in the switch. With the column ground burning out and the bad switch action, it may well be that the ignition switch was shorting in some or many positions.

If all OK, then put the ignition switch in the RUN position and one by one, jumper the others wires between the ignition connectors and record what lights and how brightly. Some will light a bit (like the dark blue ignition circuits). Let us know what you find.