Try swapping the relay with another that is the same size. Or, if you can hear the "click" coming from under the intake manifold (not the relay in the fuse box), and you have good battery voltage and your cables are in good shape....it's the starter solenoid.
I did the starter DIY. Is your GX VVTI or non-VVTI? The job is way easier for non-VVTI. For VVTI (which mine is), it's a nightmare to remove the secondary air injection tubes in order to allow the rear coolant crossover pipe to come off to access the starter bolts. It was about a day of work for me for the whole thing. I also installed a secondary air injection system bypass, removed the tubes and put in blockoff plates at both ends to make it easier next time. For non VVTI you should be able to just remove the intake manifold, pull the rear coolant crossover pipe, and remove the starter without having to mess with the air injection tubes. The actual intake is pretty easy to remove (VVTI and non-VVTI).
IMO $500 is not a bad deal for how much of a pain this job is.