Have to assume a bit here.
The first time you got resistance in the circuit, but after you removed the relay it was zero ohms? So I will assume you tested the relay the first time in the socket.
The connectors have an issue and the relay is fine. Replace the pigtails for the 87 and 30 pins something bad in the connectors or the way the connect to the wire..
The 85 and 86 pin circuit only draws a fraction of an amp so even if they marginal they wont cause a problem.
In the future pull the relay and ohm it, then replace it in the socket and ohm it again. This will show where the problem is.