Good news, your alternator and battery are fine. Your starter might be fine as well. This is a very common problem in older cars and it's fixed by replacing the solenoid on the starter. Unfortunately, I'm not sure if that particular vehicle has the starter solenoid separate from the starter or not. It's possible that the only way to replace the solenoid is to replace the entire unit. If you take it to a mechanic, try to have him replace the solenoid first and you might be able to save yourself quite a bit of money. The last starter I had replaced was $135 and I did the work myself. Solenoids are on the bottom end of two digits. ($20-$50) If you hire it fixed, labor is generally about double the cost of the part.
Your first issue is that its a Toyota
I think your starter is going bad or if the engine slowly cranks over aka the grinding sound you think you hear could be a bad battery or alternator.
My car is a 2003 Toyota Highlander and it's a Auto Transmission with a V-6 3.0 liter engine . Over the course of a few months , i would turn the key to start it would not start but makes a terrible grinding and screeching sound , now if you get the sound you need to keep turning the key like 4 times to make it stop making the grinding sound and get it started , it seems it's happening more now too so What's the problem ? The best answer gets 10 points