Why would/should a "clicky starter" relay fix, fix a starter that doesn't even click?
Why not diagnose the problem before spending money attempting to fix it?
The starter circuit is amongst the simplest on the vehicle to troubleshoot.
First it's actually two circuits, a power circuit that supplies the power to the starter and a control circuit, that controls when that power is supplied to the starter motor.
The power circuit is the battery, the starter motor, and two heavy cables one between the battery negative and the bell housing, the other between the battery positive and the starter solenoid - four connections, easy to find, make sure they are clean & tight.
The control circuit is the battery, the igntion switch, the starter solenoid, and the cable that you just checked from the battery negative to the bell housing - depending on what you're country you're in and the type of transmission, there may also be safety switches between the ignition switch and the starter solenoid - automatic transmissions have a safety switch that only allows the vehicle to start in neutral or park, and some manual transmission vehicles may have a clutch safety switch that only allows the vehicle to start if the clutch is depressed.
You can test the control circuit very easily - you need a volt meter or if that's not possible a 12v test lamp.
Find the starter solenoid, it's the bump on the starter where the cables connect - there will be two cables, the big heavy one that goes to the battery positive and a smaller one with a "spade" type lug - connector your volt meter or test lamp between the spade lug and the battery negative - turn the key, does the volt meter indicate 12V or the test lamp light at full brightness?
If it does, your problem is either in the starter or the solenoid - if it does not, your problem is in the control circuit - work your way back through the switches until you find the problem.
One last comment - the "clicky starter" relay fix only addresses one of the possible reasons that a starter clicks without starting the engine, there are at least four others - follow the steps I outlined and you WILL find why the starter does not work, fit a "clicky starter" relay fix and you have a 25% chance of fixing the click, and you haven't even started on the other possible causes.