OK, here we go. Remove the engine wiring harness connector from the bulkhead connector under the hood. I think it is the middle connector of the 3.
With the DMM, check continuity between pins "P" and "N". With ignition switch off, it will be open. Turn switch to "Run" position, it should be ZERO ohms or very close to it. Kind of wiggle the key to see if the contacts are intermittent. If this checks OK, on to the next step.
Now check continuity between pins "P" and "Q". This checks the START position and you may need a helper to hold the key in the start position. Again, wiggle the key a bit to check for intermittent contacts. Once again, it should be ZERO ohms or very close. Also while doing this check, you can also check that YELLOW wire that broke at the starter relay. You should have continuity (ZERO or near) between both "P" and "Q" and the Yellow wire.
If all these checks indicate that your Ignition Switch is good, then your problem is the engine wiring harness/connectors. Report back and we can go further if necessary.