Yours is automatic, right?

The relay is wired such that the indicator light can be working OK and still no juice to the solenoid.

After you re-solder the relay, try this: The solenoid makes a distinct "click" when is energizes. It energizes when the key hits position II (run), whether or not the engine is running. With things quiet, get an ear down below the driver's seat under the car and turn on (or get a helper) the ignition, don't start it. Listen for the click. No click = bum solenoid. Yes click = wiring problem. Lots of places to check, first the wire under the car to the solenoid, then the wires into the shifter well.

Good Luck,

Bob

:>)